public class MyNetworkClient {
    public async Task ConnectAsync(string address) {
        await this.MakeTheActualConnection(address);
        this.BeginReceiveLoop();
    }

    // It's async void! But is that bad?
    // I know that an unhandled exception here is going to bring down the process, but where else do you want
    // that exception to go? There's no external control flow that can reasonably receive such an exception.
    private async void BeginReceiveLoop() {
        while (true) {
            var incomingBlock = await this.networkStream.ReadAsync();
            if (incomingBlock == null) {
                // Disconnected or disposed
                return;
            } else {
                this.DoSomething(incomingBlock);
            }
        }
    }
}