How can we trust results computed by a third party, or the integrity of data stored by such a party? This is a classic question in systems security, and it is particularly relevant today, as much computation is now outsourced: it is performed by machines that are rented, remote, or both. Various solutions have been proposed that make assumptions about the class of computations, the failure modes of the performing computer, etc. However, deep results in theoretical computer science - interactive proofs (IPs) [3, 9, 10, 13, 19] and probabilistically checkable proofs (PCPs) [1, 2] (coupled with cryptographic commitments [11, 12] in the context of arguments ) - tell us that a fully general solution exists that makes no assumptions about the third party: the local computer can check the correctness of a remotely executed computation by inspecting a succinct proof returned by the third party. The rub is practicality: if implemented naively, the theory would be preposterously expensive (e.g., trillions of CPU-years or more to verify simple computations). Over the last several years, a number of projects have brought this theory to near-practicality in the context of implemented systems [4, 6-8, 14-18, 20-22]. The pace of progress has been rapid, and there have been many encouraging developments in this emerging area of proof-based verifiable computation. My talk will cover the high-level problem, the theory that solves the problem in principle, the projects that have reduced the theory to near-practicality and implemented it, and open questions for the area. My hope is to communicate the excitement surrounding all of the projects in the area.