If your part requires strength, rigidity, or high-temperature tolerance, then thermoplastics are a great option to fabricate your production component or prototype. Thermoplastic composites are staples in Additive Manufacturing (AM). Their use is widespread and accounts for the largest volume of 3D printed materials. Accessible property ranges of current material formulations are limited, and thus there is high interest in extending AM to high-performance engineering polymers and nanocomposites that have yet to gain wide commercial acceptance in AM. Current applications of high-performance thermoplastic polymers are limited to adaptations from conventional plastics processing such as injection molding, thermoforming, extrusion, and others. Thermoplastic composites can be categorized into particle-, fiber-, and nanomaterial-based composites as well as polymer blends. The importance of these different composite systems to AM is discussed in this review. Also reviewed are trends in instrument development such as in-nozzle impregnation, dual print heads, and higher temperature FDM that improve the printing of thermoplastic composites. An overview of newer types of AM techniques allowing higher filler loading for thermoplastic composites like liquid deposition modeling (LDM) sometimes known as direct ink writing (DIW) is discussed. Finally, a perspective is given on the important parameters and standards needed to make AM printed objects from polymer composites more effective in cost/performance ratio.