Adult-onset neurodegenerative diseases are among the most difficult human health conditions to model for drug development. Most genetic or toxin-induced cell and animal models cannot faithfully recapitulate pathology in disease-relevant cells, making it excessively challenging to explore the potential mechanisms underlying sporadic disease. Patient-derived induced pluripotent stem cells (iPSCs) can be differentiated into disease-relevant neurons, providing an unparalleled platform for in vitro modelling and development of therapeutic strategies. Here, we review recent progress in generating Alzheimer's, Parkinson's and Huntington's disease models from patient-derived iPSCs. We also describe novel discoveries of pathological mechanisms and drug evaluations that have used these patient iPSC-derived neuronal models. Additionally, current human iPSC technology allows researchers to model diseases with 3D brain organoids, which are more representative of tissue architecture than traditional neuronal cultures. We discuss remaining challenges and emerging opportunities for the use of three-dimensional brain organoids in modelling brain development and neurodegeneration.