Liquid chromatography coupled with mass spectrometry (LC-MS) is widely used to identify and quantify peptides in complex biological samples. In particular, label-free shotgun proteomics is highly effective for the identification of peptides and subsequently obtaining a global protein profile of a sample. As a result, this approach is widely used for discovery studies. Typically, the objective of these discovery studies is to identify proteins that are affected by some condition of interest (e.g. disease, exposure). However, for complex biological samples, label-free LC-MS proteomics experiments measure peptides and do not directly yield protein quantities. Thus, protein quantification must be inferred from one or more measured peptides. In recent years, many computational approaches to relative protein quantification of label-free LC-MS data have been published. In this review, we examine the most commonly employed quantification approaches to relative protein abundance from peak intensity values, evaluate their individual merits, and discuss challenges in the use of the various computational approaches.