Astronomical time series are special in that time sampling in them is uneven yet often with periodic gaps due to daytime, moon and seasons. There is therefore a need for special-purpose time-series analysis (TSA) methods. The emergence of massive CCD photometric surveys from the ground and space raises the question of an automatic period search in ≫ 105 light curves. We caution that already at the planning stage it is important to account for the effects of time sampling and analysis methods on the sensitivity of detections. We present a transparent scheme for the classification of period-search methods. We employ tools for evaluating the performance of those methods, according to the type of light curves investigated. In particular we consider sinusoidal and non-sinusoidal oscillations as well as eclipse or transit light curves. From these considerations we draw recommendations for the optimum analysis of astronomical time series. We present briefly the capability of an automatic period-search package Tatry. Finally we discuss the role of Monte Carlo simulations in the analysis of detection sensitivity. As an example, we demonstrate a practical method to account for the bandwidth (multi-trial) penalty in the statistical evaluation of detected periods.