Many modern online services feature personalized recommendations. A central challenge when providing such recommendations is that the reason why an individual user accesses the service may change from visit to visit or even during an ongoing usage session. To be effective, a recommender system should therefore aim to take the users' probable intent of using the service at a certain point in time into account. In recent years, researchers have thus started to address this challenge by incorporating intent-awareness into recommender systems. Correspondingly, a number of technical approaches were put forward, including diversification techniques, intent prediction models or latent intent modeling approaches. In this paper, we survey and categorize existing approaches to building the next generation of Intent-Aware Recommender Systems (IARS). Based on an analysis of current evaluation practices, we outline open gaps and possible future directions in this area, which in particular include the consideration of additional interaction signals and contextual information to further improve the effectiveness of such systems.