This article surveys the literature, over the period 2010-2020, on measurement of power consumption and relevant power models of virtual entities as they apply to the telco cloud. Hardware power meters are incapable of measuring power consumption of individual virtual entities co-hosted on a physical machine. Thus, software power meters are inevitable, yet their development is difficult. Indeed, there is no direct approach to measurement and, therefore, modeling through proxies of power consumption must be used. In this survey, we present trends, fallacies and pitfalls. Notably, we identify limitations of the widely-used linear models and the progression towards Artificial Intelligence / Machine Learning techniques as a means of dealing with the seven major dimensions of variability: workload type; computer virtualization agents; system architecture and resources; concurrent, co-hosted virtualized entities; approaches towards attribution of power consumption to virtual entities; frequency; and temperature.