We have reviewed the applicability of microtremor measurements to evaluate site response of soft soils. To this end, we evaluated three different techniques commonly used to estimate site effects from microtremor measurements: interpretation of Fourier amplitude spectra, computation of spectral ratios relative to a firm reference station, and, finally, computation of spectral ratios of horizontal components relative to the vertical component of ground motion (Nakamura's technique). These techniques are applied to microtremor records obtained in three cities in Mexico: Mexico City, Oaxaca, and Acapulco. These cities differ in their local geological conditions and in their seismotectonic environment. In order to evaluate the results obtained from microtremor measurements, we compare them with standard spectral ratios of the intense, S-wave part of weak or strong motion records obtained at the same sites. Our results showed that microtremor measurements can be used to estimate the dominant period of a site with very acceptable reliability in the range 0.3 to 5 Hz. The best results were obtained with Nakamura's technique, which also gives a rough estimate of amplification of seismic waves when the local geology is relatively simple. Simple numerical simulations indicate that the underlying assumptions of Nakamura's technique are consistent with the propagation of Rayleigh waves. These simple numerical simulations also explain why different researchers have been able to successfully characterize 1D site effects using microtremor records, regardless of whether they consider microtremors to consist of surface or body waves. Our results strongly suggest that the technique by Nakamura effectively compensates for source effects in microtremor measurements, which eliminates a major limitation to their application in earthquake engineering.