A brief account is given of the major difficulties which arise in measuring the specific heat of a fluid near its critical temperature, namely (a) gravity (b) temperature gradients (c) impurities. The influence of each of these disturbances is discussed in detail. Experimental techniques used in the Soviet Union and in the West to overcome the difficulties are described, and their effectiveness is assessed. Particular attention is paid to an analysis of the stirring process used in the Soviet Union. Recent high-resolution measurements for argon, ethane, and CO2 are surveyed, and the results compared with theoretical calculations for the lattice-gas model. It is suggested that the choice of the order parameter in the two-phase region is a matter of major importance. There is reasonable agreement between experiment and theory if a suitable choice is made.