Long-term culture and monitoring of individual multicellular spheroids and embryoid bodies (EBs) remains a challenge for in vitro cell propagation. Here, we used a continuous 3D projection printing approach - with an important modification of nonlinear exposure - to generate concave hydrogel microstructures that permit spheroid growth and long-term maintenance, without the need for spheroid transfer. Breast cancer spheroids grown to 10 d in the concave structures showed hypoxic cores and signs of necrosis using immunofluorescent and histochemical staining, key features of the tumor microenvironment in vivo. EBs consisting of induced pluripotent stem cells (iPSCs) grown on the hydrogels demonstrated narrow size distribution and undifferentiated markers at 3 d, followed by signs of differentiation by the presence of cavities and staining of the three germ layers at 10 d. These findings demonstrate a new method for long-term (e.g. beyond spheroid formation at day 2, and with media exchange) 3D cell culture that should be able to assist in cancer spheroid studies as well as embryogenesis and patient-derived disease modeling with iPSC EBs.