This talk has two distinct but related parts. First, I will discuss a new Grothendieck topology (the arc topology) on the category of schemes and its usefulness in addressing some foundational questions in etale cohomology (including excision as well as new proofs of the Fujiwara-Gabber theorem and some results of Huber). Secondly, I will explain how to prove the analog of the Artin vanishing theorem in rigid analytic geometry. (Joint work with Akhil Mathew.)