By admixing a fraction of exact exchange (EXX), hybrid DFT provides a more accurate and reliable description of electronic structure than traditional semi-local DFT (density functional theory). However, the conventional reciprocal-space EXX evaluation is cubic scaling and computationally demanding (typically 10x–100x more expensive than semi-local DFT), which limits the applicability of hybrid DFT. To overcome this bottleneck, we have developed an accurate linear-scaling approach that exploits the sparsity of the EXX interaction using a localized representation of the occupied space. For crystalline systems with general k-point sampling, further optimization can be made to exploit both locality and periodicity.