There are several physical reasons for anisotropic mechanical properties in additively manufactured metals. These include but are not limited to directionally dependent grain and phase morphology; crystallographic texture; directional porosity/defects; and heterogeneity associated with the melt pool, layer wise microstructure. All of these are prevalent in most additive manufacturing processes, and it is difficult to separate out the role that each play in the mechanical anisotropy. This review focuses on studies that have attempted to or reasonably isolate one or two of these sources rather than simply report on trends in mechanical properties. This is not an exhaustive review covering all additive process or mechanical properties; the main assessment is on laser powder bed fusion (LPBF) metals and tensile test results (modulus, yield strength, ultimate tensile strength (UTS), elongation, and fracture surface analysis). In summary, the primary sources of anisotropic tensile properties for LPBF alloys are crystallographic texture, anisotropic microstructure morphologies, lack of fusion defects, and the melt pool macrostructure. Within anisotropic microstructures, elongated grains appear to be secondary compared to the preferential distribution of phases and features (e.g., grain boundary alpha, precipitates, etc.). Anisotropic modulus and yield strength are primarily caused by crystallographic texture. This is supported by crystal plasticity simulations. Anisotropic elongation is primarily caused by anisotropic microstructure morphologies, lack of fusion defects, and melt pool macrostructure. The evidence to support this comes from fracture surfaces that follow these features. Melt pool macrostructure is the most challenging to experimentally isolate from the list of other sources of anisotropy. Strategies to characterize and manipulate crystallographic texture, porosity, grain and phase morphology, and melt pool macrostructures are required to better understand and control mechanical anisotropy in AM metals.