In the field of edge-cloud computing environments, there is a continuous quest for new and simplified methods to automate the deployment and runtime adaptation to application lifecycle changes. Towards that end, cloud providers promote their own service description languages to describe deployment and adaptation processes, whereas application developers opt for cloud-agnostic open standards capable of modeling applications. However, not all open standards are able to capture concepts that relate to the adaptation of the underlying computing environment to changes in the application lifecycle. In our quest for a formal approach to encapsulate these concepts, this study presents various Cloud Modeling Languages (CMLs). In this study, when referring to CMLs, we are discussing service description languages, domain-specific languages, and open standards. The output of this study is a review that performs a classification on CMLs based on their effectiveness in describing deployment and adaptation of applications in both cloud and edge environments. According to our findings, approximately 90.9% of the examined languages offer support for deployment descriptions overall. In contrast, only around 27.2% of examined languages allow developers the choice to specify whether their application components should be deployed on the edge or in a cloud environment. Regarding runtime adaptation descriptions, approximately 54.5% of the languages provide support in general.