In this talk we will discuss the hydrostatic Euler equations, which describe the leading order behavior of an ideal fluid moving in a narrow domain and are the simplest model for the thin layer equations. More precisely, we will apply an elementary method to prove that smooth solutions with a certain class of initial data will blow up in finite time. If time permits, other recent joint works with Igor Kukavica, Nader Masmoudi, Robert M. Strain, and Vlad Vicol will be discussed as well.