AbstractI was among those who proposed problem solving methods (PSMs) in the late 1970s and early 1980s as a knowledge-level description of strategies useful in building knowledge-based systems. This paper summarizes the evolution of my ideas in the last two decades. I start with a review of the original ideas. From an artificial intelligence (AI) point of view, it is not PSMs as such, which are essentially high-level design strategies for computation, that are interesting, but PSMs associated with tasks that have a relation to AI and cognition. They are also interesting with respect to cognitive architecture proposals such as Soar and ACT-R: PSMs are observed regularities in the use of knowledge that an exclusive focus on the architecture level might miss, the latter providing no vocabulary to talk about these regularities. PSMs in the original conception are closely connected to a specific view of knowledge: symbolic expressions represented in a repository and retrieved as needed. I join critics of this view, and maintain with them that most often knowledge is not retrieved from a base as much as constructed as needed. This criticism, however, raises the question of what is in memory that is not knowledge as traditionally conceived in AI, but can support theconstructionof knowledge in predicate–symbolic form. My recent proposal about cognition and multimodality offers a possible answer. In this view, much of memory consists of perceptual and kinesthetic images, which can be recalled during deliberation and from which internal perception can generate linguistic–symbolic knowledge. For example, from a mental image of a configuration of objects, numerous sentences can be constructed describing spatial relations between the objects. My work on diagrammatic reasoning is an implemented example of how this might work. These internal perceptions on imagistic representations are a new kind of PSM.