The primary motor cortex (M1) is known for its general static correspondence between body parts and clustered sites on the physical cortical sheet – the somatotopic map. Under this view, it’s tempting to believe that the orchestration of motor output in M1 is as rigid as manipulating the movement of a marionette, where a fixed set of strings would reliably dictate the movements of corresponding body parts of the puppet. In this thesis work, we argue that motor representation on the M1 cortical sheet is in fact dynamic, from two perspectives: (1) the relationship between neural activity and muscle output is dynamic along movement execution; (2) the information-bearing neural activity itself is dynamically patterned across the cortical sheet during movement execution. The first part of the work shows that, rather than being a static mapping, the relationship between neural activity and muscle output is constantly evolving during simple point-to-point reaches. Any given location on the cortical sheet bears the most information about different muscles at different times; any muscle is represented by different cortical locations at different times. Furthermore, this dynamic representation is movement-specific and most stable around movement onset, possibly serving functional needs. These dynamics happen at significantly shorter time scales than training-induced neural plasticity, presumably reflecting neural multiplexing unfolding over time. The second part of the work shows that during movement execution M1 recruits spatially organized patterns of activity across the cortical sheet in a behaviorally specific manner. In particular, recruitment times form planar propagating patterns across the cortical sheet. The directions of those propagating patterns differ systematically according to reach directions, bearing important kinematic information. This finding expands the repertoire of spatio-temporally complex neural codes and points to their potential facilitative roles in neural computation. Together, this work speaks to the dynamic motor representation of the physical M1 cortical sheet. The effects that cortical activities have on the motor outputs are best understood by considering the interplay between space and time in characterizing population neural activity, and by considering the dynamic mapping between the cortex and effectors.