Membranes can significantly reduce energy consumption during concentration of black liquor (BL) in the Kraft papermaking process, but the harsh conditions (pH similar to 12, 80 degrees C-95 degrees C, similar to 15 wt% solids) make this challenging. We elucidate challenges and opportunities for membranes in BL applications. We critically review membrane materials, processes, and operational modes investigated in the literature. Future advances will involve fabrication of higher-rejecting (95% lignin and inorganics), BL-resistant, NF, and RO membranes. Opportunities exist for molecular sieving and electrically driven membranes to recover other valuable chemicals such as carboxylic acids. We also discuss the economics of BL concentration with a single-stage membrane process.