A thermodynamics-based description, in the form of an extended phase diagram, of melting and solid-state amorphization is proposed which brings out the parallels between these two phenomena and suggests that their underlying causes are apparently the same. Through molecular dynamics simulations we demonstrate that every crystal, in principle, can undergo two different types of melting transitions with characteristic features that are also observed in radiation- and hydrogenation-induced amorphization experiments on ordered alloys. The first type, defined in terms of free energies, is shown to involve the heterogeneous nucleation of the liquid or amorphous phase at extended lattice defects (such as grain boundaries, free surfaces, voids, or dislocations) and subsequent thermally-activated propagation of solid-liquid/amorphous interfaces through the crystal. The second type, arising from a mechanical instability limit described by Born, is homogeneous and does not require thermally-activated atom mobility. It is suggested that the role of chemical and structural disordering, a prerequisite for irradiation- but not hydrogenation-induced solid-state amorphization, is merely to drive the crystal lattice to a critical combination of volume and temperature at which the amorphous phase can form either heterogeneously or homogeneously.