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 inter-chromosomal translocations and long-range intra-chromosomal SVs (>1Mb) 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. Importantly, we show that EagleC can uniquely capture a set of fusion genes that are missed by WGS or nanopore. Furthermore, EagleC also effectively captures SVs in other chromatin interaction platforms, such as HiChIP, ChIA-PET, and capture Hi-C. We apply EagleC in over 100 cancer cell lines and primary tumors, and identify a valuable set of high-quality SVs. Finally, we demonstrate that EagleC can be applied to single-cell Hi-C and used to study the SV heterogeneity in primary tumors.