Three vertical ocean carbon pumps have been known for almost three decades to sequester atmospheric carbon in the deep-water and sediment reservoirs, i.e. the solubility pump, the carbonate pump, and the soft-tissue (also known as organic, or biological) carbon pump (BCP). These three pumps maintain the vertical gradient in total dissolved inorganic carbon between the surface and deep waters. The more recently proposed microbial carbon pump (MCP) would maintain a gradient between short- and long-lived dissolved organic carbon (DOC; average lifetimes of <100 and >100 years, respectively). Long-lived DOC is an additional proposed reservoir of sequestered carbon in the ocean. This review: examines critically aspects of the vertical ocean carbon pumps and the MCP, in particular their physical dimensions and their potential roles in carbon sequestration; normalises the dimensions of the MCP to allow direct comparisons with the three vertical ocean carbon pumps; compares the MCP and vertical ocean carbon pumps; organises in a coherent framework the information available in the literature on refractory DOC; explores the potential effects of the globally changing ocean on the MCP; and identifies the assumptions that generally underlie the MCP studies, as bases for future research. The study: proposes definitions of terms, expressions and concepts related to the four ocean carbon pumps (i.e. three vertical pumps and MCP); defines the magnitude for the MCP as the rate of production of DOC with an average lifetime of >100 years and provides its first estimate for the World Ocean, i.e. 0.2 Pg C year−1; and introduces an operational “first-time-sequestration” criterion that prevents organic carbon fluxes from being assigned to both the BCP and the MCP. In our review of the potential effects of predicted climate-related changes in the ocean environment on the MCP, we found that three of the seven predicted changes could potentially enhance carbon sequestration by the MCP, and three could diminish it.