Recommender systems can strongly influence which information we see online, e.g, on social media, and thus impact our beliefs, decisions, and actions. At the same time, these systems can create substantial business value for different stakeholders. Given the growing potential impact of such AI-based systems on individuals, organizations, and society, questions of fairness have gained increased attention in recent years. However, research on fairness in recommender systems is still a developing area. In this survey, we first review the fundamental concepts and notions of fairness that were put forward in the area in the recent past. Afterwards, we provide a survey of how research in this area is currently operationalized, for example, in terms of the general research methodology, fairness metrics, and algorithmic approaches. Overall, our analysis of recent works points to certain research gaps. In particular, we find that in many research works in computer science very abstract problem operationalizations are prevalent, which circumvent the fundamental and important question of what represents a fair recommendation in the context of a given application.