Single-cell omics technologies are currently solving biological and medical problems that earlier have remained elusive, such as discovery of new cell types, cellular differentiation trajectories and communication networks across cells and tissues. Current advances especially in single-cell multi-omics hold high potential for breakthroughs by integration of multiple different omics layers. To pair with the recent biotechnological developments, many computational approaches to process and analyze single-cell multi-omics data have been proposed. In this review, we first introduce recent developments in single-cell multi-omics in general and then focus on the available data integration strategies. The integration approaches are divided into three categories: early, intermediate, and late data integration. For each category, we describe the underlying conceptual principles and main characteristics, as well as provide examples of currently available tools and how they have been applied to analyze single-cell multi-omics data. Finally, we explore the challenges and prospective future directions of single-cell multi-omics data integration, including examples of adopting multi-view analysis approaches used in other disciplines to single-cell multi-omics.