We investigate the damage mechanisms of amorphous and low semicrystalline semiaromatic polyamides, polyphthalamides (PPA), and two other amorphous polymers, polycarbonate (PC) and poly(methyl methacrylate) (PMMA), under tensile deformation. Ultrasmall-angle X-ray scattering (USAXS) experiments allow us to describe the beginning of the damage and the growth of crazes. Interpreting the results allows us to measure the volume fractions of damages, as well as their distribution of sizes at different stages of tensile deformation. Different modes of damage are observed. They are initiated by the nucleation of nanometric crazes around preexisting defects for PC, PMMA, and the amorphous polyamide. Then, the growth of these crazes is blocked by the strain hardening at the local level. By increasing the strain further, the growth of a second family of large crazes is observed for these three polymers before the yielding, which leads to fracture for PC and PMMA far in the macroscopic strain hardening regime, but not for the amorphous polyamide for which damaged is stabilized after the stress softening and in the ensuing necking regime for which strain hardening is also observed. In the case of two low semicrystalline polyamides, no damage is observed at all and deformation takes place by necking without damaging and breaking. We propose interpretations for these different behaviors.