Because of its numerous advantages: coverage of wide spectral ranges, consistency of wave numbers, high resolution, high signal to noise ratio, etc., Fourier transform spectrometry has been and is still widely used in molecular spectroscopy, producing large amounts of new precise spectroscopic data. The analyses of these data have led to a deep understanding of the very fine effects (resonances, centrifugal distortion, etc.) which affect both the line positions and intensities. As an illustration of progress achieved, using Fourier transform spectra, in the spectroscopy of asymmetric tops, examples concerning ozone, hydrogen peroxide and nitrogen dioxide are described.