What happens if a finally block throws an exception?

If a finally block throws an exception, what exactly happens?

Specifically, what happens if the exception is thrown midway through a finally block. Do the rest of statements (after) in this block get invoked?

I am aware that exceptions will propagate upwards.

If a finally block throws an exception what exactly happens ?

That exception propagates out and up, and will (can) be handled at a higher level.

Your finally block will not be completed beyond the point where the exception is thrown.

If the finally block was executing during the handling of an earlier exception then that first exception is lost.

C# 4 Language Specification § 8.9.5: If the finally block throws another exception, processing of the current exception is terminated.

For questions like these I usually open up an empty console application project in Visual Studio and write a small sample program:

using System;

class Program
{
    static void Main(string[] args)
    {
        try
        {
            try
            {
                throw new Exception("exception thrown from try block");
            }
            catch (Exception ex)
            {
                Console.WriteLine("Inner catch block handling {0}.", ex.Message);
                throw;
            }
            finally
            {
                Console.WriteLine("Inner finally block");
                throw new Exception("exception thrown from finally block");
                Console.WriteLine("This line is never reached");
            }
        }
        catch (Exception ex)
        {
            Console.WriteLine("Outer catch block handling {0}.", ex.Message);
        }
        finally
        {
            Console.WriteLine("Outer finally block");
        }
    }
}

When you run the program you will see the exact order in which catch and finally blocks are executed. Please note that code in the finally block after the exception is being thrown will not be executed (in fact, in this sample program Visual Studio will even warn you that it has detected unreachable code):

Inner catch block handling exception thrown from try block.
Inner finally block
Outer catch block handling exception thrown from finally block.
Outer finally block

Additional Remark

As Michael Damatov pointed out, an exception from the try block will be "eaten" if you don't handle it in an (inner) catch block. In fact, in the example above the re-thrown exception does not appear in the outer catch block. To make that even more clear look at the following slightly modified sample:

using System;

class Program
{
    static void Main(string[] args)
    {
        try
        {
            try
            {
                throw new Exception("exception thrown from try block");
            }
            finally
            {
                Console.WriteLine("Inner finally block");
                throw new Exception("exception thrown from finally block");
                Console.WriteLine("This line is never reached");
            }
        }
        catch (Exception ex)
        {
            Console.WriteLine("Outer catch block handling {0}.", ex.Message);
        }
        finally
        {
            Console.WriteLine("Outer finally block");
        }
    }
}

As you can see from the output the inner exception is "lost" (i.e. ignored):

Inner finally block
Outer catch block handling exception thrown from finally block.
Outer finally block