Three-dimensional (3D), submillimeter-scale constructs of neural cells, known as cortical spheroids, are of rapidly growing importance in biological research because these systems reproduce complex features of the brain in vitro. Despite their great potential for studies of neurodevelopment and neurological disease modeling, 3D living objects cannot be studied easily using conventional approaches to neuromodulation, sensing, and manipulation. Here, we introduce classes of microfabricated 3D frameworks as compliant, multifunctional neural interfaces to spheroids and to assembloids. Electrical, optical, chemical, and thermal interfaces to cortical spheroids demonstrate some of the capabilities. Complex architectures and high-resolution features highlight the design versatility. Detailed studies of the spreading of coordinated bursting events across the surface of an isolated cortical spheroid and of the cascade of processes associated with formation and regrowth of bridging tissues across a pair of such spheroids represent two of the many opportunities in basic neuroscience research enabled by these platforms.