The Hi-C technique has been shown to be a promising method to detect structural variations (SVs) in human genomes. However, algorithms that can use Hi-C data for a full-range SV detection have been severely lacking. Current methods can only identify interchromosomal translocations and long-range intrachromosomal SVs (>1 Mb) at less-than-optimal resolution. Therefore, we develop EagleC, a framework that combines deep-learning and ensemble-learning strategies to predict a full range of SVs at high resolution. We show that EagleC can uniquely capture a set of fusion genes that are missed by whole-genome sequencing or nanopore. Furthermore, EagleC also effectively captures SVs in other chromatin interaction platforms, such as HiChIP, Chromatin interaction analysis with paired-end tag sequencing (ChIA-PET), and capture Hi-C. We apply EagleC in more than 100 cancer cell lines and primary tumors and identify a valuable set of high-quality SVs. Last, we demonstrate that EagleC can be applied to single-cell Hi-C and used to study the SV heterogeneity in primary tumors.