The frontal polymerization (FP) of carbon/epoxy (C/Ep) composites is investigated, considering FP as a viable route for the additive manufacturing (AM) of thermoset composites. Neat epoxy (Ep) resin-, short carbon fiber (SCF)-, and continuous carbon fiber (CCF)-reinforced composites are considered in this study. The evolution of the exothermic reaction temperature, polymerization frontal velocity, degree of cure, microstructures, effects of fiber concentration, fracture surface, and thermal and mechanical properties are investigated. The results show that exothermic reaction temperatures range between 110 °C and 153 °C, while the initial excitation temperatures range from 150 °C to 270 °C. It is observed that a higher fiber content increases cure time and decreases average frontal velocity, particularly in low SCF concentrations. This occurs because resin content, which predominantly drives the exothermic reaction, decreases with increased fiber content. The FP velocities of neat Ep resin- and SCF-reinforced composites are seen to be 0.58 and 0.50 mm/s, respectively. The maximum FP velocity (0.64 mm/s) is observed in CCF/Ep composites. The degree of cure (αc) is observed to be in the range of 70% to 85% in FP-processed composites. Such a range of αc is significantly low in comparison to traditional composites processed through a long cure cycle. The glass transition temperature (Tg) of neat epoxy resin is seen to be approximately 154 °C, and it reduces slightly to a lower value (149 °C) for SCF-reinforced composites. The microstructures show significantly high void contents (12%) and large internal cracks. These internal cracks are initiated due to high thermal residual stress developed during curing for non-uniform temperature distribution. The tensile properties of FP-cured samples are seen to be inferior in comparison to autoclave-processed neat epoxy. This occurs mostly due to the presence of large void contents, internal cracks, and a poor degree of cure. Finally, a highly efficient and controlled FP method is desirable to achieve a defect-free microstructure with improved mechanical and thermal properties.