The fundamental thermodynamic bound for the specific energy consumption (SEC) of seawater desalination is independent of mechanism and relates to work-driven processes (exemplified by reverse osmosis, RO). There is a corresponding method-independent constrained thermodynamic bound for heat-driven desalination, e.g., multi-effect and multi-stage flash distillation, along with thermal vapor compression. Similar constrained limits exist when the finite capacity of heat or work reservoirs must be accounted for. We elucidate basic insights and consequences of these mechanism-independent limits relative to the measured performance of the most efficient seawater desalination plants, specifically: (1) the dramatic differences in SEC between RO and thermal desalination as well as the degree to which each of them differs from their respective basic performance bounds, (2) the strikingly different dependence of the SEC of RO vs. thermal desalination on feedwater salinity and feedwater temperature, and (3) the magnitudes and sources of potential reductions in SEC. The SEC of nature's thermal desalination scheme (the solar-rainfall cycle) is also estimated. © 2016 Elsevier B.V..