Modern software systems intensively use the Agile software development processes for their development and maintenance. The Agile development methodology encourages customer satisfaction, early incremental delivery, and overall development simplicity. Agile development methods accept changes in requirements and technology and use a more adaptive or iterative approach to planning. With the adaptation of Agile process models in the development of modern software systems, there is a need for continuous improvement in the Agile processes. Agile development processes are modified and upgraded by utilizing software metrics. There are several proposed software metrics for measuring performance and quality in Agile software development. These include customer satisfaction, story point estimation, velocity, test coverage, defects in production, and other metrics. Each software metric has its own merits and demerits. This research aims to provide a comprehensive review of published research work on software metrics. Specifically, it summarizes the software metrics used for measuring the performance of Agile process models. This research paper will help understand the usefulness of various software metrics used in Agile development, and it will serve as a foundation for future research in software metrics for Agile software development.