The availability of single crystals of superconducting cuprates has made measurements of a number of physical properties of these highly anisotropic systems possible. However, in spite of major developments in crystallization techniques and a massive literature on the growth process, there is generally considerable variation in the critical temperature obtained from transport, magnetic or optical measurement. Certain persistent problems arising during the crystal growth process are examined and analyzed in an attempt to isolate factors influencing physical properties. In this context we review the growth of YBa2Cu3O7-δ (123) crystals from nonstoichiometric melts, emphasizing impurity effects and complexities of the oxygenation process, using as an example the substitution of Ca in the 123 single crystals. Finally we look critically at the measurements themselves as a means of evaluating crystal quality. © 1990, Elsevier Science Publishers B.V. (North-Holland). All rights reserved.