Reciprocal recommender systems~(RRS), conducting bilateral recommendations between two involved parties, have gained increasing attention for enhancing matching efficiency. However, the majority of existing methods in the literature still reuse conventional ranking metrics to separately assess the performance on each side of the recommendation process. These methods overlook the fact that the ranking outcomes of both sides collectively influence the effectiveness of the RRS, neglecting the necessity of a more holistic evaluation and a capable systemic solution. In this paper, we systemically revisit the task of reciprocal recommendation, by introducing the new metrics, formulation, and method. Firstly, we propose five new evaluation metrics that comprehensively and accurately assess the performance of RRS from three distinct perspectives: overall coverage, bilateral stability, and balanced ranking. These metrics provide a more holistic understanding of the system's effectiveness and enable a comprehensive evaluation. Furthermore, we formulate the RRS from a causal perspective, formulating recommendations as bilateral interventions, which can better model the decoupled effects of potential influencing factors. By utilizing the potential outcome framework, we further develop a model-agnostic causal reciprocal recommendation method that considers the causal effects of recommendations. Additionally, we introduce a reranking strategy to maximize matching outcomes, as measured by the proposed metrics. Extensive experiments on two real-world datasets from recruitment and dating scenarios demonstrate the effectiveness of our proposed metrics and approach. The code and dataset are available at: https://github.com/RUCAIBox/CRRS.

Many social services including online dating, social media, recruitment and online learning, largely rely on \matching people with the right people". The success of these services and the user experience with them often depends on their ability to match users. Reciprocal Recommender Systems (RRS) arose to facilitate this process by identifying users who are a potential match for each other, based on information provided by them. These systems are inherently more complex than user-item recommendation approaches and unidirectional user recommendation services, since they need to take into account both users' preferences towards each other in the recommendation process. This entails not only predicting accurate preference estimates as classical recommenders do, but also defining adequate fusion processes for aggregating user-to-user preferential information. The latter is a crucial and distinctive, yet barely investigated aspect in RRS research. This paper presents a snapshot analysis of the extant literature to summarize the state-of-the-art RRS research to date, focusing on the fundamental features that differentiate RRSs from other classes of recommender systems. Following this, we discuss the challenges and opportunities for future research on RRSs, with special focus on (i) fusion strategies to account for reciprocity and (ii) emerging application domains related to social recommendation.