ARCH and GARCH models are discrete time models that accommodate the important real-world phenomenon of "volatilities" that change over time. These are now often viewed as examples of the general class of stochastic volatility models, though that term is also used to describe a group of specific continuous-time models whose discrete analogs share common ground with the ARCH and GARCH models.
Over the course of the semester I will build up a collection of expositions and original resources. To begin the collection we start with two informative surveys:
F. Armerin, "Stochastic Volatility:A Gentle Introduction"
P. Jakel, "Stochastic Volatility Models: Past, Present and Future" (a PP presentation)