While plastic deformation of high symmetry crystals, such as metallic crystals, is well-studied, plasticity in low symmetry molecular crystals received much less attention. We investigate the physical basis of plastic deformation in the energetic molecular crystal HMX. We use atomistic simulations to evaluate the stress-dislocation velocity relation for various types of dislocations, and perform homogenization to calibrate the strain rate sensitivity (SRS) of the HMX crystal. Further, we study the constitutive behavior of shear bands which exhibits shear thinning (strong dependence on strain rate) and weak temperature dependence. This information is collected in a constitutive description for crystal plasticity of HMX.