Metal additive manufacturing (MAM) is an emerging technology to produce complex end-use metallic parts. To adopt MAM for manufacturing numerous engineering parts used in critical applications, a thorough understanding of the relationship between the complex thermal cycles in MAM and the unique heterogeneous microstructures of MAM parts need to be established. This review article provides a comprehensive overview of the evolution of heterogeneous microstructures in MAM parts, including melt pool boundaries, heterogeneous grain structure, sub-grain cellular structure, matrix supersaturation, segregation, phase transformation, oxides formation, and texture. The evolution of residual stresses and the anisotropy in MAM parts and the post-MAM heat treatment effects on the microstructural evolution are also discussed. This review covers the microstructural aspects of most engineering materials in particular steels, high entropy alloys, aluminum alloys, titanium alloys, nickel-base superalloys, and copper alloys, with a primary focus on the parts manufactured using selective laser melting, direct energy deposition, and electron beam melting processes.