According to Robert K. Wysocki, there are 4 quadrants of PM methodologies.
If the Goal is Clear and Solution is Clear, we use Traditional Project Management (TPM). eg. linear processes and typical waterfull method.
If the Goal is Clear and Solution is not Clear, we use Agile Project Management (APM). eg. Iterative and Adaptive project management processes.
If the Goal is Not Clear and Solution is Not Clear, we use Extreme Project Management (xPM). eg. cure the common cold through various means. However, are we really curing the common cold?
If the Goal is Not Clear and Solution is Clear, we use Emertxe Project Management (MPx).
Which is your most commonly used PM methodology? For me, they are TPM and APM.
If the project's goal and solution are both not clear, it is really a huge challenge for the Project Manager.