The mathematical transforms used in Phase-Locked Loops (PLLs) play a crucial role in their performance and functioning. Depending on the format of the control loop's input signal, noise level requirements and other requirements such as available computational power, one must choose which topology best suits a given application. This article will address the most used transforms and filters in the most common PLL topologies, such as the Clarke Transform, the Park Transform, the Second-Order Generalized Integrator (SOGI) filter and the Hilbert Transform. Finally, a comparison of the advantages and disadvantages of each of these methods is discussed.