Few month ago I have developed an attribute that restricts methods or controllers to specific domains.

It is quite easy to use:

[IsDomain("localhost","example.com","www.example.com","*.t1.example.com")]
[HttpGet("RestrictedByHost")]
public IActionResult Test(){}

You can also apply it directly on a controller.

public class IsDomainAttribute : Attribute, Microsoft.AspNetCore.Mvc.Filters.IAuthorizationFilter
{

    public IsDomainAttribute(params string[]  domains)
    {
        Domains = domains;
    }

    public string[] Domains { get; }

    public void OnAuthorization(AuthorizationFilterContext context)
    {
        var host = context.HttpContext.Request.Host.Host;
        if (Domains.Contains(host))
            return;
        if (Domains.Any(d => d.EndsWith("*"))
                && Domains.Any(d => host.StartsWith(d.Substring(0, d.Length - 1))))
            return;
        if (Domains.Any(d => d.StartsWith("*"))
                && Domains.Any(d => host.EndsWith(d.Substring(1))))
            return;

        context.Result = new Microsoft.AspNetCore.Mvc.NotFoundResult();//.ChallengeResult
    }
}

Restriction: you may not be able to have two same routes on different methods with different filters I mean the following may throw an exception for duplicate route:

[IsDomain("test1.example.com")]
[HttpGet("/Test")]
public IActionResult Test1(){}

[IsDomain("test2.example.com")]
[HttpGet("/Test")]
public IActionResult Test2(){}

I created library for subdomain routing which you can create such a route. It is working currently for a .NET Core 1.1 and .NET Framework 4.6.1 but will be updated in near future. This is how is it working:
1) Map subdomain route in Startup.cs

public void Configure(IApplicationBuilder app, IHostingEnvironment env, ILoggerFactory loggerFactory)
{
    var hostnames = new[] { "localhost:54575" };

    app.UseMvc(routes =>
    {
        routes.MapSubdomainRoute(
            hostnames,
            "SubdomainRoute",
            "{username}",
            "{controller}/{action}",
            new { controller = "Home", action = "Index" });
    )};

2) Controllers/HomeController.cs

public IActionResult Index(string username)
{
    //code
}

3) That lib will also allow you to generate URLs and forms. Code:

@Html.ActionLink("User home", "Index", "Home" new { username = "user1" }, null)

Will generate <a href="http://user1.localhost:54575/Home/Index">User home</a> Generated URL will also depend on current host location and schema.
You can also use html helpers for BeginForm and UrlHelper. If you like you can also use new feature called tag helpers (FormTagHelper, AnchorTagHelper)
That lib does not have any documentation yet, but there are some tests and samples project so feel free to explore it.

In ASP.NET Core, the host is available via Request.Host.Host. If you want to allow overriding the host via a query parameter, first check Request.Query.

To cause a host query parameter to propagate into to new route-based URLs, add this code to the app.UseMvc route configuration:

routes.Routes.Add(new HostPropagationRouter(routes.DefaultHandler));

And define HostPropagationRouter like this:

/// <summary>
/// A router that propagates the request's "host" query parameter to the response.
/// </summary>
class HostPropagationRouter : IRouter
{
    readonly IRouter router;

    public HostPropagationRouter(IRouter router)
    {
        this.router = router;
    }

    public VirtualPathData GetVirtualPath(VirtualPathContext context)
    {
        if (context.HttpContext.Request.Query.TryGetValue("host", out var host))
            context.Values["host"] = host;
        return router.GetVirtualPath(context);
    }

    public Task RouteAsync(RouteContext context) => router.RouteAsync(context);
}

If you are looking at giving MultiTenancy capabilities to your project with different domains/subdomains for each tenant, you should have a look at SaasKit:

https://github.com/saaskit/saaskit

Code examples can be seen here: http://benfoster.io/blog/saaskit-multi-tenancy-made-easy

Some examples using ASP.NET core: http://andrewlock.net/forking-the-pipeline-adding-tenant-specific-files-with-saaskit-in-asp-net-core/

EDIT: If you do no want to use SaasKit in your ASP.NET core project you can have a look at Maarten's implementation of domain routing for MVC6: https://blog.maartenballiauw.be/post/2015/02/17/domain-routing-and-resolving-current-tenant-with-aspnet-mvc-6-aspnet-5.html

However those Gists are not maintained and need to be tweaked to work with the latest release of ASP.NET core.

Direct link to the code: https://gist.github.com/maartenba/77ca6f9cfef50efa96ec#file-domaintemplateroutebuilderextensions-cs

After defining a new Route handler that would look at the host passed in the URL, you can go with the idea of a base Controller that is aware of the Site it’s being accessed for. It looks like this:

public abstract class SiteController : Controller {
    ISiteProvider _siteProvider;

    public SiteController() {
        _siteProvider = new SiteProvider();
    }

    public SiteController(ISiteProvider siteProvider) {
        _siteProvider = siteProvider;
    }

    protected override void Initialize(RequestContext requestContext) {
        string[] host = requestContext.HttpContext.Request.Headers["Host"].Split(':');

        _siteProvider.Initialise(host[0]);

        base.Initialize(requestContext);
    }

    protected override void OnActionExecuting(ActionExecutingContext filterContext) {
        ViewData["Site"] = Site;

        base.OnActionExecuting(filterContext);
    }

    public Site Site {
        get {
            return _siteProvider.GetCurrentSite();
        }
    }

}

ISiteProvider is a simple interface:

public interface ISiteProvider {
    void Initialise(string host);
    Site GetCurrentSite();
}

I refer you go to Luke Sampson Blog

To capture the subdomain when using Web API, override the Action Selector to inject a subdomain query parameter. Then use the subdomain query parameter in your controllers' actions like this:

public string Get(string id, string subdomain)

This approach makes debugging convenient since you can specify the query parameter by hand when using localhost instead of the actual host name (see the standard MVC5 routing answer for details). This is the code for Action Selector:

class SubdomainActionSelector : IHttpActionSelector
{
    private readonly IHttpActionSelector defaultSelector;

    public SubdomainActionSelector(IHttpActionSelector defaultSelector)
    {
        this.defaultSelector = defaultSelector;
    }

    public ILookup<string, HttpActionDescriptor> GetActionMapping(HttpControllerDescriptor controllerDescriptor)
    {
        return defaultSelector.GetActionMapping(controllerDescriptor);
    }

    public HttpActionDescriptor SelectAction(HttpControllerContext controllerContext)
    {
        var routeValues = controllerContext.Request.GetRouteData().Values;
        if (!routeValues.ContainsKey("subdomain")) {
            string host = controllerContext.Request.Headers.Host;
            int index = host.IndexOf('.');
            if (index >= 0)
                controllerContext.Request.GetRouteData().Values.Add("subdomain", host.Substring(0, index));
        }
        return defaultSelector.SelectAction(controllerContext);
    }
}

Replace the default Action Selector by adding this to WebApiConfig.Register:

config.Services.Replace(typeof(IHttpActionSelector), new SubdomainActionSelector(config.Services.GetActionSelector()));

To capture the subdomain while retaining the standard MVC5 routing features, use the following SubdomainRoute class derived from Route.

Additionally, SubdomainRoute allows the subdomain optionally to be specified as a query parameter, making sub.example.com/foo/bar and example.com/foo/bar?subdomain=sub equivalent. This allows you to test before the DNS subdomains are configured. The query parameter (when in use) is propagated through new links generated by Url.Action, etc.

The query parameter also enables local debugging with Visual Studio 2013 without having to configure with netsh or run as Administrator. By default, IIS Express only binds to localhost when non-elevated; it won't bind to synonymous hostnames like sub.localtest.me.

class SubdomainRoute : Route
{
    public SubdomainRoute(string url) : base(url, new MvcRouteHandler()) {}

    public override RouteData GetRouteData(HttpContextBase httpContext)
    {
        var routeData = base.GetRouteData(httpContext);
        if (routeData == null) return null; // Only look at the subdomain if this route matches in the first place.
        string subdomain = httpContext.Request.Params["subdomain"]; // A subdomain specified as a query parameter takes precedence over the hostname.
        if (subdomain == null) {
            string host = httpContext.Request.Headers["Host"];
            int index = host.IndexOf('.');
            if (index >= 0)
                subdomain = host.Substring(0, index);
        }
        if (subdomain != null)
            routeData.Values["subdomain"] = subdomain;
        return routeData;
    }

    public override VirtualPathData GetVirtualPath(RequestContext requestContext, RouteValueDictionary values)
    {
        object subdomainParam = requestContext.HttpContext.Request.Params["subdomain"];
        if (subdomainParam != null)
            values["subdomain"] = subdomainParam;
        return base.GetVirtualPath(requestContext, values);
    }
}

For convenience, call the following MapSubdomainRoute method from your RegisterRoutes method just as you would plain old MapRoute:

static void MapSubdomainRoute(this RouteCollection routes, string name, string url, object defaults = null, object constraints = null)
{
    routes.Add(name, new SubdomainRoute(url) {
        Defaults = new RouteValueDictionary(defaults),
        Constraints = new RouteValueDictionary(constraints),
        DataTokens = new RouteValueDictionary()
    });
}

Finally, to conveniently access the subdomain (either from a true subdomain or a query parameter), it is helpful to create a Controller base class with this Subdomain property:

protected string Subdomain
{
    get { return (string)Request.RequestContext.RouteData.Values["subdomain"]; }
}

This is not my work, but I had to add it on this answer.

Here is a great solution to this problem. Maartin Balliauw wrote code that creates a DomainRoute class that can be used very similarly to the normal routing.

http://blog.maartenballiauw.be/post/2009/05/20/ASPNET-MVC-Domain-Routing.aspx

Sample use would be like this...

routes.Add("DomainRoute", new DomainRoute( 
    "{customer}.example.com", // Domain with parameters 
    "{action}/{id}",    // URL with parameters 
    new { controller = "Home", action = "Index", id = "" }  // Parameter defaults 
))

;

You can do it by creating a new route and adding it to the routes collection in RegisterRoutes in your global.asax. Below is a very simple example of a custom Route:

public class ExampleRoute : RouteBase
{

    public override RouteData GetRouteData(HttpContextBase httpContext)
    {
        var url = httpContext.Request.Headers["HOST"];
        var index = url.IndexOf(".");

        if (index < 0)
            return null;

        var subDomain = url.Substring(0, index);

        if (subDomain == "user1")
        {
            var routeData = new RouteData(this, new MvcRouteHandler());
            routeData.Values.Add("controller", "User1"); //Goes to the User1Controller class
            routeData.Values.Add("action", "Index"); //Goes to the Index action on the User1Controller

            return routeData;
        }

        if (subDomain == "user2")
        {
            var routeData = new RouteData(this, new MvcRouteHandler());
            routeData.Values.Add("controller", "User2"); //Goes to the User2Controller class
            routeData.Values.Add("action", "Index"); //Goes to the Index action on the User2Controller

            return routeData;
        }

        return null;
    }

    public override VirtualPathData GetVirtualPath(RequestContext requestContext, RouteValueDictionary values)
    {
        //Implement your formating Url formating here
        return null;
    }
}

Yes but you have to create your own route handler.

Typically the route is not aware of the domain because the application could be deployed to any domain and the route would not care one way or another. But in your case you want to base the controller and action off the domain, so you will have to create a custom route that is aware of the domain.