Even though the asynchronous design methodology is considered to be a promising solution to upcoming challenges of designing complex integrated circuits (ICs), it is not widely accepted by the industry. Besides the lack of mature design tools, a further key inhibitor of using this design style is the widespread assumption that asynchronous circuits are difficult to test due to problems with system timing during test, nondeterminism, and difficulties with applying standard test approaches such as scan. However, there is a huge variety of approaches to handle these testing issues. This paper summarizes the different available test methodologies for asynchronous and globally-asynchronous locally-synchronous (GALS) designs and addresses their strengths and weaknesses. Moreover, it gives an overview of a methodology for testing based on the use of specific test processor, developed by IHP.