RNA molecules are folded into structures and complexes to perform a wide variety of functions. Determination of RNA structures and their interactions is a fundamental problem in RNA biology. Most RNA molecules in living cells are large and dynamic, posing unique challenges to structure analysis. Here we review progress in RNA structure analysis, focusing on methods that use the "cross-link, proximally ligate, and sequence" principle for high-throughput detection of base-pairing interactions in living cells. Beginning with a comparison of commonly used methods in structure determination and a brief historical account of psoralen cross-linking studies, we highlight the important features of cross-linking methods and new biological insights into RNA structures and interactions from recent studies. Further improvement of these cross-linking methods and application to previously intractable problems will shed new light on the mechanisms of the "modern RNA world."