PID control stands for Proportional, Integral and Derivative control. PID controllers have been around since about 1940. Modern controllers perform the same functions as those, perhaps with a few embelishments and certainly more accurately, but the same functions nonetheless.
PID controllers are the best general purpose controllers to do the job. More sophisticated control algorithms will produce better performance when fitted to a specific process, but poorer performance results if the process changes. This sensitivity to process changes is called robustness, with more robust being less sensitive. The PID algorithm is an excellent trade-off between robustness and performance.
Although theory on PID-controllers is widespread and more or less uniform nowadays, in practice there are many algorithms and parameter settings. The 20-sim Control library, supports the most common algorithms.