Methods and systems for growing algae are disclosed. For example, disclosed is an exemplary bioreactor for growing algae that includes a chamber, a liquid-permeable membrane that includes a plurality of hollow fiber membranes disposed within the chamber. Each hollow fiber membrane can include a hollow interior and may be made of a liquid-permeable, algae-impermeable membrane, and each hollow fiber membrane may be disposed within the chamber. The respective interiors of the hollow fiber membranes may at least partially define an inner-capillary space (ICS). The interior of the chamber and respective exteriors of the hollow fiber membranes may at least partially define an extra-capillary space (ECS). When algae is grown in the ECS, lipids produced by the algae may be extracted from the ECS to the ICS via the hollow fiber membranes without killing the majority of algae and while containing the algae to the ECS.