This article provides an overview of frequency-domain spectral fitting methods for one-dimensional magnetic resonance spectra (MRS) in vivo. Methods presented range from simple peak integration, curve-fitting based on different line-shape models, through to linear combination minimization routines that make extensive use of prior knowledge and simulated or acquired 'basis sets' of spectra from constituent compounds. It is shown that the choice of analysis method depends strongly on the type of data to be analyzed, with the simpler methods working best on relatively sparse spectra with minimal peak overlap and cross-correlation. Quantification accuracy is critically dependent on data acquisition and analysis parameters. Uncertainty estimates are discussed, and analyses of human MRS data are exemplified. MRS can give accurate and reproducible concentration estimates of many metabolites with relatively small signals, provided that appropriate care and attention is paid to both data acquisition and analysis protocols.