The question of apparent mass anomalies in classical cepheids was first brought up by Christy (1968) and Stobie (1969), but 15 years later there is still no definite picture concerning the reality and the possible cause of these mass anomalies. The masses obtained from application of standard evolutionary theory were always sensibly larger than the masses derived from pulsation theory using both linear and nonlinear codes. Since for various reasons few people have accepted the idea that mass loss could play an important role in cepheids a number of elaborate scenarios have been proposed to account for the mass discrepancies. Among these are helium enriched outer layers and tangled magnetic fields. It is difficult, however, to see how significant mass loss can be avoided during the evolution of the more massive cepheids. In fact, practically all supergiants lose mass over the whole HR diagram, a process frequently manifesting itself in photometric microvariability. Little hope can be placed in attempts to solve the problem by means of improved determinations of the physical parameters of cepheids; intrinsic colours, luminosities, radii, effective temperatures, and the width of the instability strip have been disputed for years with no definite results yet. Only independent observational evidence will make it possible to confirm - or reject - the mass anomalies. On account of the large number observed and because of the fairly complete sample they represent, the cepheids in the LMC, SMC and in our Galaxy are best suited for this kind of investigation.