Context: With growing software reuse and interoperability, Open Source Software (OSS) is more ubiquitous than ever. Often sourced for free from volunteer-driven work, many organizations lack any awareness of the sustainability of OSS they depend on- at least until something breaks. As awareness of this threat grows, OSS communities, governments, and enterprises are increasingly concerned about making the OSS ecosystem more sustainable in the long term. However, sustainability in OSS is not a very well-defined concept, thus making research and decisions regarding OSS adoption more difficult. Objective: Synthesize how the wider concept of OSS sustainability is currently understood “in the wild”, explore how it can be characterized, and discuss the impact a better understanding can have on adoption and development. Method: We conducted a systematic mapping study (SMS) across 111 studies from the literature to extract sustainability understandings, factors that influence it, and measures that are indicators of sustainability in OSS projects. Results: Social and technical concerns are well-explored and reaffirm the importance of the OSS community. Individual, economic, and environmental definitions remain relatively underexplored. There is a growing usage of the term “sustainability” in OSS research. We propose 19 aspects (factors that contribute to OSS sustainability and measures that indicate it) that can be utilized to understand OSS sustainability. Conclusion: Those aspects can be utilized by practitioners who rely on OSS to better understand the projects they depend upon, as well by researchers exploring this ecosystem.