Kraft black liquor, a side-stream of the pulp and paper industry, contains lignin, hemicelluloses, and cooking chemicals. This stream is typically evaporated and burned in the recovery boiler to generate power and recover the cooking chemicals used in the pulping process to digest the wood. However, the recovery boiler is often the bottleneck of the chemical-recovery process. By removing lignin from kraft black liquor, the load on the recovery boiler can be reduced, allowing the mill to increase its pulping capacity without having to invest in a new recovery boiler. Moreover, lignin recovery can generate new revenue streams for the mill by replacing fossil materials with lignin. Precipitation by acidification and membrane filtration are the main technologies for lignin fractionation and concentration from kraft black liquor. These methods allow for later valorization of lignin for the production of biofuels and biochemicals. Lignin separation by acid precipitation has been thoroughly investigated, with the most relevant issues being the type of acid used, pH, and temperature conditions for the precipitation. Based on extensive research, several commercial processes have been implemented in different pulp and paper mills worldwide. Membrane filtration has also been thoroughly investigated, with UF being the most popular choice for kraft black liquor fractionation and lignin separation. While membrane processes for lignin recovery have reached the pilot scale stage and are being evaluated economically, more research is needed to reach the commercial stage. Membrane fouling remains the main challenge that membrane filtration faces when it comes to implementation of the processes and understanding how to mitigate fouling and how to improve the cleaning process can be beneficial if membrane processes are to be implemented in pulp and paper mills. Thus, advancing membrane-based lignin recovery and valorization technologies through collaborative efforts is essential to driving the transition to renewable resources, fostering circular economy innovations, and unlocking lignin’s potential in biofuels, sustainable materials, and emerging markets.