Cosmological gravitational particle production (CGPP) is a viable production mechanism for dark matter. Spin-0, spin-1/2, spin-3/2, spin-2 fields can be produced via CGPP during inflation and reheating, and the relics can be dark matter candidates. Chapter 1 of this thesis contains the framework of CGPP, which is based on quantum field theory in curved spacetime and inflationary cosmology. Chapter 2 contains a study of CGPP in the context of alpha-attractor inflationary models. Chapter 3 contains a method for analytically evaluating CGPP of fermions, namely the Exact WKB (EWKB) method, which is based on Stokes phenomenon. Chapter 4 contains a study of CGPP of massive spin-2 fields. Chapter 5 contains a study of phenomenology of ultralight vector dark matter with nonminimal interactions with gravity.