<p>Electro-optic sampling allows the electric field of THz, mid-infrared and visible light pulses to be measured directly as a function of time, with data analysis often performed in the frequency domain after fast Fourier transform. Here, we review aspects of Fourier theory relevant to the frequency-domain analysis of light pulses recorded in the time domain. We describe a “best practise” approach to using the discrete Fourier transform that ensures consistency with analytical results from the continuous Fourier transform. We summarise a phenomenological time-domain model of THz pulses, based on carrier and envelope waves, and show that it can reproduce a wide variety of experimental single- to multi-cycle THz pulses, with exemplary data from lab-based sources (photoconductive antennae, optical rectification, spintronic emitters) and a THz free-electron laser. A quantitative comparison of the spectral energy density of these distinct sources is enabled by the amplitude-accurate discrete Fourier transform. We describe a method that ensures the accurate calculation of the absolute spectral phase (valid for arbitrary sampling windows in the time domain) and summarise how the carrier-envelope phase, pulse arrival time, and chirp can be obtained from the phase. Our aim with this overview of THz pulse analysis is to highlight algorithms and concepts that are useful to newcomers to time-domain spectroscopy and experts, alike.</p>