Primary cilia (PC) are non-motile dynamic microtubule-based organelles that protrude from the surface of most mammalian cells. They emerge from the older centriole during the G1/G0 phase of the cell cycle, while they disassemble as the cells re-enter the cell cycle at the G2/M phase boundary. They function as signal hubs, by detecting and transducing extracellular signals crucial for many cell processes. Similar to most cell types, all neocortical neural stem and progenitor cells (NSPCs) have been shown harboring a PC allowing them to sense and transduce specific signals required for the normal cerebral cortical development. Here, we provide detailed protocols to generate and characterize two-dimensional (2D) and three-dimensional (3D) cell-based models from human induced pluripotent stem cells (hIPSCs) to further dissect the involvement of PC during neocortical development. In particular, we present protocols to study the PC biogenesis and function in 2D neural rosette-derived NSPCs including the transduction of the Sonic Hedgehog (SHH) pathway. To take advantage of the three-dimensional (3D) organization of cerebral organoids, we describe a simple method for 3D imaging of in toto immunostained cerebral organoids. After optical clearing, rapid acquisition of entire organoids allows detection of both centrosomes and PC on neocortical progenitors and neurons of the whole organoid. Finally, we detail the procedure for immunostaining and clearing of thick free-floating organoid sections preserving a significant degree of 3D spatial information and allowing for the high-resolution acquisition required for the detailed qualitative and quantitative analysis of PC biogenesis and function.