DevOps is a very trendy term these days in the software development companies (SDC), term that emerges as a possible solution to finally reach an acceleration and a rise of productivity expected with the appearance of agile development approaches, but that until now had not materialized, through automation practices, continuous integration, continuous build, and continuous deployment. This paper aims to show current knowledge about the process of adopting DevOps in SDC through a systematic mapping of the literature. However, the results obtained show that there is little detailed information regarding activities, tasks, roles, and other important process elements for the adoption of DevOps. Similarly, it has been concluded that there is no a unified terminology, therefore, it is important to standardize it to simplify the understanding and application of DevOps. Furthermore, this paper shows the preview of the framework that it is being developed for the adoption of DevOps in the SDC.