Hybrid density functionals (hybrids) have emerged as a practical reference method for ab initio electronicstructure-based simulations because they resolve several known accuracy issues of lower levels of density-functional theory (DFT) while offering affordable computational cost on current highperformance computers. There are two main computational bottlenecks for atomistic simulations using hybrid DFT: evaluating the non-local exact exchange contribution and finding the solution of a generalized eigenvalue problem (matrix diagonalization). Here, we discuss advances and perspectives for both challenges as recently implemented in the all-electron code FHI-aims .