How do I get client IP address in ASP.NET CORE?

Some fallback logic can be added to handle the presence of a Load Balancer.

Also, through inspection, the X-Forwarded-For header happens to be set anyway even without a Load Balancer (possibly because of additional Kestrel layer?):

public string GetRequestIP(bool tryUseXForwardHeader = true)
{
    string ip = null;

    // todo support new "Forwarded" header (2014) https://en.wikipedia.org/wiki/X-Forwarded-For

    // X-Forwarded-For (csv list):  Using the First entry in the list seems to work
    // for 99% of cases however it has been suggested that a better (although tedious)
    // approach might be to read each IP from right to left and use the first public IP.
    // http://stackoverflow.com/a/43554000/538763
    //
    if (tryUseXForwardHeader)
        ip = GetHeaderValueAs<string>("X-Forwarded-For").SplitCsv().FirstOrDefault();

    // RemoteIpAddress is always null in DNX RC1 Update1 (bug).
    if (ip.IsNullOrWhitespace() && _httpContextAccessor.HttpContext?.Connection?.RemoteIpAddress != null)
        ip = _httpContextAccessor.HttpContext.Connection.RemoteIpAddress.ToString();

    if (ip.IsNullOrWhitespace())
        ip = GetHeaderValueAs<string>("REMOTE_ADDR");

    // _httpContextAccessor.HttpContext?.Request?.Host this is the local host.

    if (ip.IsNullOrWhitespace())
        throw new Exception("Unable to determine caller's IP.");

    return ip;
}

public T GetHeaderValueAs<T>(string headerName)
{
    StringValues values;

    if (_httpContextAccessor.HttpContext?.Request?.Headers?.TryGetValue(headerName, out values) ?? false)
    {
        string rawValues = values.ToString();   // writes out as Csv when there are multiple.

        if (!rawValues.IsNullOrWhitespace())
            return (T)Convert.ChangeType(values.ToString(), typeof(T));
    }
    return default(T);
}

public static List<string> SplitCsv(this string csvList, bool nullOrWhitespaceInputReturnsNull = false)
{
    if (string.IsNullOrWhiteSpace(csvList))
        return nullOrWhitespaceInputReturnsNull ? null : new List<string>();

    return csvList
        .TrimEnd(',')
        .Split(',')
        .AsEnumerable<string>()
        .Select(s => s.Trim())
        .ToList();
}

public static bool IsNullOrWhitespace(this string s)
{
    return String.IsNullOrWhiteSpace(s);
}

Assumes _httpContextAccessor was provided through DI.

The API has been updated. Not sure when it changed but according to Damien Edwards in late December, you can now do this:

var remoteIpAddress = request.HttpContext.Connection.RemoteIpAddress;

In project.json add a dependency to:

"Microsoft.AspNetCore.HttpOverrides": "2.2.0"

In Startup.cs, in the Configure() method add:

app.UseForwardedHeaders(new ForwardedHeadersOptions
{
    ForwardedHeaders = ForwardedHeaders.XForwardedFor |
    ForwardedHeaders.XForwardedProto
});  

And, of course:

using Microsoft.AspNetCore.HttpOverrides;

Then, I could get the ip by using:

Request.HttpContext.Connection.RemoteIpAddress

In my case, when debugging in VS I got always IpV6 localhost, but when deployed on an IIS I got always the remote IP.

Some useful links: How do I get client IP address in ASP.NET CORE? and RemoteIpAddress is always null

The ::1 is maybe because of:

Connections termination at IIS, which then forwards to Kestrel, the v.next web server, so connections to the web server are indeed from localhost. (https://stackoverflow.com/a/35442401/5326387)

Edit 12/2020: Thanks to SolidSnake: as of Dec 2020 the latest version is 2.2.0

Edit 06/2021: Thanks to Hakan Fıstık: In .NET 5 the namespace is Microsoft.AspNetCore.Builder