This paper is about neural mechanisms of direction selectivity (DS) in Macaque primary visual cortex, V1. We present data (on male macaque) showing strong DS in a majority of simple cells in V1 layer 4Cα, the cortical layer that receives direct afferent input from the Magnocellular division of the Lateral Geniculate Nucleus (LGN). Magnocellular LGN cells are not direction-selective. To understand the mechanisms of DS, we built a large-scale, recurrent model of spiking neurons called DSV1. Like its predecessors, DSV1 reproduces many visual response properties of V1 cells including orientation selectivity. Two important new features of DSV1 are (a) DS is initiated by small, consistent dynamic differences in the visual responses of OFF and ON Magnocellular LGN cells, and (b) DS in the responses of most model simple cells is increased over those of their feedforward inputs; this increase is achieved through dynamic interaction of feedforward and intra-cortical synaptic currents without the use of intra-cortica...