In circular accelerators, the betatron tune is measured by analysing the particle coordinates, sampled over N turns. Algorithms based either on the Average Phase Advance method or on the Fast Fourier Transform (FFT) are routinely used to compute the tune. More sophisticated approaches have recently been proposed. They rely on analytical interpolations of the FFT, as suggested by E. Asseo, or on algorithms based on continuous spectral analysis, according to the studies of J. Laskar. In this paper we critically review the various methods of measuring the tune and we present analytical estimates of the error as a function of N. The results are supported by numerical simulations carried out on both simple and complicated lattices, including nonlinear magnets. Applications to experimental data obtained in the CERN SPS are also shown.