Elasticity is a goal of cloud computing. An elastic system should manage in an autonomic way its resources, being adaptive to dynamic workloads, allocating additional resources when workload is increased and deallocating resources when workload decreases. PaaS providers should manage resources of customer applications with the aim of converting those applications into elastic services. This survey identifies the requirements that such management imposes on a PaaS provider: autonomy, scalability, adaptivity, SLA awareness, composability and upgradeability. This document delves into the variety of mechanisms that have been proposed to deal with all those requirements. Although there are multiple approaches to address those concerns, providers' main goal is maximisation of profits. This compels providers to look for balancing two opposed goals: maximising quality of service and minimising costs. Because of this, there are still several aspects that deserve additional research for finding optimal adaptability strategies. Those open issues are also discussed.