Neurodevelopmental disorders (NDs) are impairments that affect the development and growth of the brain and the central nervous system during embryonic and early postnatal life. Genetically manipulated animals have contributed greatly to the advancement of ND research, but many of them differ considerably from the human phenotype. Cellular in vitro models are also valuable, but the availability of human neuronal cells is limited and their lifespan in culture is short. Human pluripotent stem cells (hPSCs), including embryonic stem cells and induced pluripotent stem cells, comprise a powerful tool for studying developmentally regulated diseases, including NDs. We reviewed all recent studies in which hPSCs were used as in vitro models for diseases and syndromes characterized by impairment of neurogenesis or synaptogenesis leading to intellectual disability and delayed neurodevelopment. We analyzed their methodology and results, focusing on the data obtained following in vitro neural differentiation and gene expression and profiling of the derived neurons. Electrophysiological recording of action potentials, synaptic currents and response to neurotransmitters is pivotal for validation of the neuronal fate as well as for assessing phenotypic dysfunctions linked to the disease in question. We therefore focused on the studies which included electrophysiological recordings on the in vitro-derived neurons. Finally, we addressed specific issues that are critical for the advancement of this area of research, specifically in providing a reliable human pre-clinical research model and drug screening platform.