Cryovolcanic resurfacing is a popular mechanism to explain relatively young surface units on icy satellites of Jupiter, Saturn, Uranus, and Neptune. Prior to the Galileo data acquired between 1996 and 2001, Europa was thought to have undergone significant cryovolcanic resurfacing, facilitated by a global ocean beneath the icy surface. However, close examination of Galileo data at resolutions much better than those of Voyager images show that many of the features previously thought to be cryovolcanic are commonly best explained by other formative mechanisms, including tectonism and diapirism. In this study, I present an examination of the characteristics of a variety of Europan surface features for which effusive cryovolcanism is a possible origin, including apparently lobate flows, certain elliptical to circular lenticulae, and low-lying, smooth, low-albedo surfaces. A review of cryovolcanic eruption theory, together with Galileo data analysis of Europan surface geology and composition, indicates that cryovolcanism is a viable, though not unequivocal, explanation for some of these features. Some constraints on cryomagma properties and lithospheric structure are offered for these cases. The presence of small-volume, low-viscosity effusions is supported by observations and modeling. Some positive relief lenticulae could represent more viscous effusions, although diapirism may be a preferable explanation. However, strong evidence is lacking for cryovolcanic resurfacing on a large scale. On the basis of our experience with Galileo images of Europa (and Ganymede), Voyager-era inferences for widespread cryovolcanism on icy satellites may be overstated and will need to be carefully reexamined in the light of new data from upcoming spacecraft missions.