•iPSCs allow modeling of neurodegenerative disorders in disease-relevant human systems.•Recapitulation of late-stage disease phenotypes remains challenging.•New strategies have emerged to advance iPSC models and tackle these challenges.•Increased cellular diversity and 3D culture allow more physiological disease models.•Editing mutations/risk factors and improving maturation may promote pathology. Induced pluripotent stem-cell-based models enable investigation of pathomechanisms in disease-relevant human brain cell types and therefore offer great potential for mechanistic and translational studies on neurodegenerative disorders, such as Alzheimer’s disease (AD). While current AD models allow analysis of early disease phenotypes including Aβ accumulation and Tau hyperphosphorylation, they still fail to fully recapitulate later hallmarks such as protein aggregation and neurodegeneration. This impedes the identification of pathomechanisms and novel therapeutic targets. We discuss strategies to overcome these drawbacks and optimize physiological properties and translational potential of iPSC-based models by improving culture formats, increasing cellular diversity, applying genome editing, and implementing maturation and ageing paradigms.