The human mind can do many amazing things. Of particular interest are a set of cognitive abilities such as simple inference and recognition that are computationally very demanding, but that we humans perform without any perceptible delay or any sense of mental effort – this despite the fact that our brains use slow, millisecond-speed components. In this position paper, I present a brief inventory of human mental operations that exhibit this kind of surprising efficiency. I suggest that we humans accomplish these feats by (a) avoiding the computationally intractable forms of these problems and (b) by applying massively parallel processing, though perhaps of a very simple kind. This is not a new suggestion – some of these ideas were first developed in my mid-1970s work on NETL [1]. However, I believe that a renewed focus on the parallel vs. serial components of mental processing can help us both in understanding human intelligence and in achieving human-like performance in our AI systems.