In fringe projection profilometry, the luminance nonlinearity of the projector has been recognized as one of the most crucial factors decreasing the measurement accuracy. It induces the ripple-like artifacts on the measured phase map. The self-adaptive correcting algorithms, i.e., self-correcting algorithms, allow us to suppress the effect of the projector nonlinearity without a prior calibration for the projector intensities or phase errors. This paper introduces the research progress in the self-correcting algorithms. Among them, the first algorithm is to determine a nonlinear curve representing the projector nonlinearity, directly from the captured fringe patterns, thus correcting the phase errors using this curve. The second one is to recognize and remove the nonlinearity-induced errors, directly from a calculated phase map. With the last one, error function coefficients are estimated from a couple of phase maps having different frequencies. Measurement results demonstrate these self-correcting algorithms to be effective in suppressing influences of the projector nonlinearity in the absence of any calibration information.