Understanding the mechanical response of polymer glasses is currently one of the biggest challenges in polymer physics and soft matter. The deformation of polymer glasses has a considerable non-affine component at the monomer-unit level, meaning that every unit within every chain undergoes an additional displacement on top of the displacement imposed by the strain tensor . We used theoretical and computational approaches, based on the non-affine molecular-level dynamics and on the vibrational density of states. A mechanistic assessment is obtained of how chemistry-dependent many-body angular constraints along the chain and cross-linking constraints affect: 1. the value of Tg (as parameterized also by the critical number of total nearest neighbour units at the transition, z* ), 2. the rate-dependent elasticity/rigidity component of response, 3. the rate-dependent energy absorption and ductility, and 4. the yielding transition . This theoretical description poses the basis of a new chemical-design platform for linking polymer chemistry to mechanical performance in advanced polymer-based functional materials.  A. Zaccone & E.M. Terentjev, Phys. Rev. Lett. (2013).  A. Lappala, A. Zaccone, E.M. Terentjev, Soft Matter (2016).  V. Palyulin, C.J. Ness, R. Milkus, R. Elder, T.Sirk, A. Zaccone, in preparation.