Shimura curves are generalizations of classical modular curves. Along with their classical counterpart, Shimura curves play a pivotal role in Wiles's proof of Fermat's Last Theorem. However, because of the lack of cusps (and hence no Fourier expansions for modular forms), computation about Shimura curves is substantially more difficult than that about modular curves. In this series of talks, I will give a quick introduction to Shimura curves and then discuss some recent development on explicit methods for Shimura curves.