Social media platforms are increasingly adopting features that display crowdsourced context alongside posts, a technique pioneered by X's Community Notes. These systems -- which we term Crowdsourced Context Systems (CCS) -- have the potential to reshape the information ecosystem as major platforms embrace them as alternatives to professional fact-checking. To understand the features and implications of these systems, we conduct a systematic literature review of existing CCS research (n=56) and analyze real-world CCS implementations. Based on our analysis, we develop a framework with two components. First, we present a theoretical model to conceptualize and define CCS. Second, we identify a design space encompassing six aspects: participation, inputs, curation, presentation, platform treatment, and transparency. We also surface normative implications of different CCS design and implementation choices. Our work integrates theoretical, design, and ethical perspectives to establish a foundation for future human-centered research on Crowdsourced Context Systems.