The demand for additively manufactured polymer composites with increased specific properties and functional microstructure has drastically increased over the past decade. The ability to manufacture complex designs that can maximize strength while reducing weight in an automated fashion has made 3D-printed composites a popular research target in the field of engineering. However, a significant amount of understanding and basic research is still necessary to decode the fundamental process mechanisms of combining enhanced functionality and additively manufactured composites. In this review, external field-assisted additive manufacturing techniques for polymer composites are discussed with respect to (1) self-assembly into complex microstructures, (2) control of fiber orientation for improved interlayer mechanical properties, and (3) incorporation of multi-functionalities such as electrical conductivity, self-healing, sensing, and other functional capabilities. A comparison between reinforcement shapes and the type of external field used to achieve mechanical property improvements in printed composites is addressed. Research has shown the use of such materials in the production of parts exhibiting high strength-to-weight ratio for use in aerospace and automotive fields, sensors for monitoring stress and conducting electricity, and the production of flexible batteries.