This chapter classifies the fundamental deformation mechanisms into five groups: 1) rate-independent plasticity by crystallographic slip, 2) rate-dependent plasticity by dislocation glide, 3) power-law creep by dislocation climb-plus-glide, 4) grain boundary sliding (GBS), and 5) diffusion creep, in accordance to Ashby and other researchers. Each deformation-mechanism constitutive equation is solved for both transient as well as steady-state deformation behaviors. It is important to note the intragranular or intergranular nature of these deformation mechanisms, because they are responsible for different types of physical damages that will be discussed in the next chapter. Last but not the least, the aforementioned fundamental deformation mechanisms are constructed into deformation-mechanisms maps for a few engineering alloys, conforming to Ashby’s format. This illustrates how the micro-mechanisms may be manifested as the dominant deformation mechanism at the macroscopic level.