Software non-functional requirements address a multitude of objectives, expectations, and even liabilities that must be considered during development and operation. Typically, these non-functional requirements originate from different domains and their concrete scope, notion, and demarcation to functional requirements is often ambiguous. In this study we seek to categorize and analyze relevant work related to software engineering in a DevOps context in order to clarify the different focus areas, themes, and objectives underlying non-functional requirements and also to identify future research directions in this field. We conducted a systematic mapping study, including 142 selected primary studies, extracted the focus areas, and synthesized the themes and objectives of the described NFRs. In order to examine non-engineering-focused studies related to non-functional requirements in DevOps, we conducted a backward snowballing step and additionally included 17 primary studies. Our analysis revealed 7 recurrent focus areas and 41 themes that characterize NFRs in DevOps, along with typical objectives for these themes. Overall, the focus areas and themes of NFRs in DevOps are very diverse and reflect the different perspectives required to align software engineering with technical quality, business, compliance, and organizational considerations. The lack of methodological support for specifying, measuring, and evaluating fulfillment of these NFRs in DevOps-driven projects offers ample opportunities for future research in this field. Particularly, there is a need for empirically validated approaches for operationalizing non-engineering-focused objectives of software.