Autism spectrum disorder (ASD) is a brain disorder that involves changes in neuronal connections. Abnormal morphology of dendritic spines on postsynaptic neurons has been observed in ASD patients and transgenic mice that model different monogenetic causes of ASD. A number of ASD-associated genetic variants are known to disrupt dendritic local protein synthesis, which is essential for spine morphogenesis, synaptic transmission, and plasticity. Most of our understanding on the molecular mechanism underlying ASD depends on studies using rodents. However, recent advance in human pluripotent stem cells and their neural differentiation provides a powerful alternative tool to understand the cellular aspects of human neurological disorders. In this review, we summarize recent progress on studying mRNA targeting and local protein synthesis in stem cell-derived neurons, and discuss how perturbation of these processes may impact synapse development and functions that are relevant to cognitive deficits in ASD.