The adoption of continuous software engineering practices such as DevOps (Development and Operations) in business operations has contributed to significantly shorter software development and deployment cycles. Recently, the term MLOps (Machine Learning Operations) has gained increasing interest as a practice that brings together data scientists and operations teams. However, the adoption of MLOps in practice is still in its infancy and there are few common guidelines on how to effectively integrate it into existing software development practices. In this paper, we conduct a systematic literature review and a grey literature review to derive a framework that identifies the activities involved in the adoption of MLOps and the stages in which companies evolve as they become more mature and advanced. We validate this framework in three case companies and show how they have managed to adopt and integrate MLOps in their large-scale software development companies. The contribution of this paper is threefold. First, we review contemporary literature to provide an overview of the state-of-the-art in MLOps. Based on this review, we derive an MLOps framework that details the activities involved in the continuous development of machine learning models. Second, we present a maturity model in which we outline the different stages that companies go through in evolving their MLOps practices. Third, we validate our framework in three embedded systems case companies and map the companies to the stages in the maturity model.