What is the correct way to handle exceptions and UnobservedTaskException in the TPL?

Information from: A Task's exception(s) were not observed either by Waiting on the Task or accessing its Exception property. As a result, the unobserved exception was

If you create a Task, and you don't ever call task.Wait() or try to retrieve the result of a Task<T>, when the task is collected by the garbage collector, it will tear down your application during finalization. For details, see MSDN's page on Exception Handling in the TPL.

The best option here is to "handle" the exception. This can be done via a continuation - you can attach a continuation to the task, and log/swallow/etc the exception that occurs. This provides a clean way to log task exceptions, and can be written as a simple extension method, ie:

public static void LogExceptions(this Task task)
{
    task.ContinueWith( t =>
    {
         var aggException = t.Exception.Flatten();
         foreach(var exception in aggException.InnerExceptions)
             LogException(exception);
    }, 
    TaskContinuationOptions.OnlyOnFaulted);
}

With the above, you can prevent any task from tearing down the app, and logging it, via:

Task.Factory.StartNew( () => 
   { 
       // Do your work...
   }).LogExceptions();

Alternatively, you can subscribe to the TaskScheduler.UnobservedTaskException and handle it there.

Continuation of the task could determine the status of the parent task whether it get faulted or completed to success. A continuation can find out if an exception was thrown by the antecedent Task by the antecedent task's exception property. The following code snippet will print the results of a NullReferenceException to the console.

Task task1 = Task.Factory.StartNew (() => { throw null; });
Task task2 = task1.ContinueWith (ant => Console.Write(ant.Exception());

If task1 throws an exception and this exception is not captured/queried by the continuation then it is considered unhandled and the application get halted. With continuations it is enough to establish the result of the task via the Status property.

asyncTask.ContinueWith(task =>
{
    // Check task status.
    switch (task.Status)
    {
        // Handle any exceptions to prevent UnobservedTaskException.             
        case TaskStatus.RanToCompletion:
            if (asyncTask.Result)
            {
                // Do stuff...
            }
            break;
        case TaskStatus.Faulted:
            if (task.Exception != null)
                mainForm.progressRightLabelText = task.Exception.InnerException.Message;
            else
                mainForm.progressRightLabelText = "Operation failed!";
        default:
            break;
    }
}

If you don't use continuations you either have to wait on the task in a try/catch block or query a task's Result in a try/catch block. See below code snippet:

int x = 0;
Task<int> task = Task.Factory.StartNew (() => 7 / x);
try
{
    task.Wait();
    // OR.
    int result = task.Result;
}
catch (AggregateException aggEx)
{
    Console.WriteLine(aggEx.InnerException.Message);
}