BACKGROUND: The relationship between body mass (M) and standard metabolic rate (B) among living organisms remains controversial, though it is widely accepted that in many cases B is approximately proportional to the three-quarters power of M. RESULTS: The biological significance of the straight-line plots obtained over wide ranges of species when B is plotted against log M remains a matter of debate. In this article we review the values ascribed to the gradients of such graphs (typically 0.75, according to the majority view), and we assess various attempts to explain the allometric power-law phenomenon, placing emphasis on the most recent publications. CONCLUSION: Although many of the models that have been advanced have significant attractions, none can be accepted without serious reservations, and the possibility that no one model can fit all cases has to be more seriously entertained.