This paper considers feedforward carrier frequency estimation methods in burst-mode digital transmission, with tutorial objectives foremost. Assuming PSK modulation, two scenarios are envisaged in which frequency estimates are derived either from a preamble appended to the data block, or directly from the modulated signal. Several estimation algorithms are considered with different and somewhat contrasting characteristics. The characteristics we focus on are: estimation accuracy, estimation range, minimum operating signal-to-noise ratio (threshold), and implementation complexity. They provide a framework within which current estimation methods can be evaluated. The paper reviews and compares some prominent algorithms proposed in literature, trying to single out the best ones for a given application.