Designing software compatible with cloud-based Microservice Architectures (MSAs) is vital due to the performance, scalability, and availability limitations. As the complexity of a system increases, it is subject to deprecation, difficulties in making updates, and risks in introducing defects when making changes. Microservices are small, loosely coupled, highly cohesive units that interact to provide system functionalities. We provide a comprehensive survey of current research into ways of identifying services in systems that can be redeployed as microservices. Static, dynamic, and hybrid approaches have been explored. While code analysis techniques dominate the area, dynamic and hybrid approaches remain open research topics.