Everyday spatial problems such as tying shoelaces, untangling cables, locating objects, opening doors, matching shapes, finding routes, solving puzzles, … are embedded in 3-dimensional physical space and their solutions need to be manifested in physical space. Such problems can be solved either directly in space by means of perception and manipulation or they can be transformed into abstract representations in order to be solved by reasoning or computation and subsequently transformed back into physical space. In my contribution I will compare the two approaches and I will discuss how they can be combined. I will introduce the notion of mild abstraction as a way of combining the best features of both worlds, present a variety of forms of mild abstraction, demonstrate their uses for spatial problem solving, and propose that mild abstraction can be exploited for non-spatial domains, as well.