Recent advancements in artificial intelligence (AI) and the emergence of AI-based social applications in the market have propelled research on the possibility of consumers developing relationships with AI. Motivated by the diversity of approaches and inconsistent findings in this emerging research stream, this systematic literature review analyzes 37 peer-reviewed empirical studies focusing on human-AI relationships published between 2018 and 2023. We identify three major theoretical domains (social psychology, communication and media studies, and human-machine interactions) as foundations for conceptual development, and detail theories used in the reviewed papers. Given the radically new nature of social AI innovation, we recommend developing a novel theoretical approach that would synergistically utilize cross-disciplinary literature. Analysis of the methodology indicates that quantitative studies dominate this research stream, while qualitative, longitudinal, and mixed-method approaches are used infrequently. Examination of research models and variables used in the studies suggests the need to reconceptualize factors and processes of human-AI relationship, such as agency, autonomy, authenticity, reciprocity, and empathy, to better correspond to the social AI context. Based on our analysis, we propose an integrative conceptual framework and offer directions for future research that incorporate the need to develop a comprehensive theory of human -AI relationships, explore the nomological networks of its key constructs, and implement methodological variety and triangulation.