Memory Cache in dotnet core

The constructor is:

using Microsoft.Extensions.Caching.Memory;

. . .

MemoryCache myCache = new MemoryCache(new MemoryCacheOptions());

_{My answer is focused on the "Within .Net core I could not find System.Runtime.Cache", as I run into this same issue. For using IMemoryCache with the specific OP's scenario, the accepted answer is great.}

There are two completely different caching implementations/solutions:

1 - System.Runtime.Caching/MemoryCache
2 - Microsoft.Extensions.Caching.Memory/IMemoryCache

System.Runtime.Caching/MemoryCache:
This is pretty much the same as the old day's ASP.Net MVC's HttpRuntime.Cache. You can use it on ASP.Net CORE without any dependency injection. This is how to use it:

// First install 'System.Runtime.Caching' (NuGet package)

// Add a using
using System.Runtime.Caching;

// To get a value
var myString = MemoryCache.Default["itemCacheKey"];

// To store a value
MemoryCache.Default["itemCacheKey"] = myString;

Microsoft.Extensions.Caching.Memory
This one is tightly coupled with Dependency Injection. This is one way to implement it:

// In asp.net core's Startup add this:
public void ConfigureServices(IServiceCollection services)
{
    services.AddMemoryCache();
}

Using it on a controller:

// Add a using
using Microsoft.Extensions.Caching.Memory;

// In your controller's constructor, you add the dependency on the 'IMemoryCache'
public class HomeController : Controller
{
    private IMemoryCache _cache;
    public HomeController(IMemoryCache memoryCache)
    {
        _cache = memoryCache;
    }

    public void Test()
    {
        // To get a value
        string myString = null;
        if (_cache.TryGetValue("itemCacheKey", out myString))
        { /*  key/value found  -  myString has the key cache's value*/  }


        // To store a value
        _cache.Set("itemCacheKey", myString);
    }
}

As pointed by @WillC, this answer is actually a digest of Cache in-memory in ASP.NET Core documentation. You can find extended information there.