All perceptual and cognitive circuits in the human cerebral cortex are organized into layers. Specializations of a canonical laminar network of bottom-up, horizontal, and top-down pathways carry out multiple kinds of biological intelligence across different neocortical areas. This article describes what this canonical network is and notes that it can support processes as different as 3D vision and figure-ground perception; attentive category learning and decision-making; speech perception; and cognitive working memory (WM), planning, and prediction. These processes take place within and between multiple parallel cortical streams that obey computationally complementary laws. The interstream interactions that are needed to overcome these complementary deficiencies mix cell properties so thoroughly that some authors have noted the difficulty of determining what exactly constitutes a cortical stream and the differences between streams. The models summarized herein explain how these complementary properties arise, and how their interstream interactions overcome their computational deficiencies to support effective goal-oriented behaviors.