Abstract: Weinstein domains are symplectic analogs of smooth handlebodies and come equipped with decompositions with elementary symplectic pieces. As a result, they are easy to construct, have computable invariants, and include classical examples like cotangent bundles. After giving some background, I will survey several questions (and recent answers) about Weinstein domains, many of which are motivated by analogous questions in smooth topology. For example, I will discuss the partial analog of the h-cobordism theorem for Weinstein domains (and why the full h-cobordism theorem fails) and explain a symplectic analog of topological localization à la Sullivan and Quillen, which can be used to interpolate between symplectic flexibility and rigidity. No background in symplectic geometry will be assumed.