Liquid chromatography-mass spectrometry is widely used for comparative replicate sample analysis in proteomics, lipidomics and metabolomics. Before statistical comparison, registration must be established to match corresponding analytes from run to run. Alignment, the most popular correspondence approach, consists of constructing a function that warps the content of runs to most closely match a given reference sample. To date, dozens of correspondence algorithms have been proposed, creating a daunting challenge for practitioners in algorithm selection. Yet, existing reviews have highlighted only a few approaches. In this review, we describe 50 correspondence algorithms to facilitate practical algorithm selection. We elucidate the motivation for correspondence and analyze the limitations of current approaches, which include prohibitive runtimes, numerous user parameters, model limitations and the need for reference samples. We suggest and describe a paradigm shift for overcoming current correspondence limitations by building on known liquid chromatography-mass spectrometry behavior. 