In this talk, I will cover some exciting progress on constructing efficient PCPs. My work gives a systematic way to construct PCPs, improving upon the state-of-the-art PCP constructions from nearly 20 years ago. This implies that many well-known approximation algorithms are nearly-optimal under well-believed complexity-theoretic conjectures. In the process, we also solve various conjectures in property testing and distributed computing. These advances are facilitated by the newly-emerging theory of high-dimensional expansion and draw upon connections with various areas of theoretical computer science and mathematics.