The arrival process of bidders and bids in online auctions is important for studying and modeling supply and demand in the online marketplace. Whereas bid arrivals are observable in online auction data, bidder behavior is typically not. A popular assumption in the online auction literature is that a homogeneous Poisson bidder arrival process is a reasonable approximation. This approximation underlies statistical models and simulations used in eld studies. However, empirical research has shown that the process of bid arrivals is far from homogeneous, as it features early and last-moment bidding, as well as a self-similar structure. In this chapter we discuss two types of models: Descriptive models for bid arrivals that were derived based on features of real bid data in online auctions, and models for bidder arrivals that lead to the bid arrival process. The model for the bid arrival process, called the BARISTA process, can generate dierent intensities at dierent stages of the auctions. We discuss its properties, show how to simulate bid arrivals from it, and how to estimate its parameters. We then describe two bidder behavior models that lead to versions of the BARISTA process. Model adequacy and performance are illustrated via simulation and real data from eBay.