SUMMARY Highly accurate protein structure predictors have generated hundreds of millions of protein structures; these pose a challenge in terms of storage and processing. Here, we present Foldcomp, a novel lossy structure compression algorithm, and indexing system to address this challenge. By using a combination of internal and Cartesian coordinates and a bi-directional NeRF-based strategy, Foldcomp improves the compression ratio by a factor of three compared to the next best method. Its reconstruction error of 0.08 Å is comparable to the best lossy compressor. It is five times faster than the next fastest compressor and competes with the fastest decompressors. With its multi-threading implementation and a Python interface that allows for easy database downloads and efficient querying of protein structures by accession, Foldcomp is a powerful tool for managing and analysing large collections of protein structures. AVAILABILITY AND IMPLEMENTATION Foldcomp is a free open-source software (GPLv3) and available for Linux, macOS, and Windows at https://foldcomp.foldseek.com. Foldcomp provides the AlphaFold Swiss-Prot (2.9GB), TrEMBL (1.1TB), and ESMatlas HQ (114GB) database ready-for-download.