Oxygen reduction reaction (ORR) and evolution reaction (OER) are one pair of the most important electrochemical reactions associated with energy conversion and storage technologies, such as fuel cells, metal–air batteries, and water electrolyzers. However, the sluggish ORR and OER requires a significantly large quantity of precious metals (e.g., Pt or Ir) to enhance reaction activity and durability. Highly active and robust nonprecious metal catalysts (NPMCs) are desperately required to address the cost and durability issues. Among NPMC formulations studied, carbon-based catalysts hold the greatest promise to replace these precious metals in the future due to their low-cost, extremely high surface area, excellent mechanical and electrical properties, sufficient stability under harsh environments, and high functionality. In particular, nitrogen-doped carbon nanocomposites, which were prepared from “metal-free” N–C formulations and transition metals-derived M–N–C (M=Fe or Co), have demonstrated remarkably improved catalytic activity and stability in alkaline and acidic electrolytes. In this review, based on the recent progress in the field, we aim to provide an overview for both types of carbon catalysts in terms of catalyst synthesis, structure/morphology, and catalytic activity and durability enhancement. We primarily focus on elucidation of synthesis–structure–activity correlations obtained from synthesis and extensive characterization, thereby providing guidance for rational design of advanced catalysts for the ORR. Additionally, a hybrid concept of using highly ORR active carbon nanocomposites to support Pt nanoparticles was highlighted with an aim to enhance catalytic performance and reduce required precious metal loading. Beyond the ORR, opportunities and challenges of ORR/OER bifunctional carbon composite catalysts were outlined. Perspectives on these carbon-based catalysts, future approaches, and possible pathways to address current remaining challenges are also discussed.