The typical abnormalities observed in the brain of Alzheimer's disease (AD) patients include synaptic alterations, neuronal death, brain inflammation, and the accumulation of protein aggregates in the form of amyloid plaques and neurofibrillary tangles. Despite the development of many animal and in vitro models for AD, there is a lack of an experimental approach that fully recapitulates essential aspects of the disease in human cells. Here, we report the generation of a new model to study AD, consisting of cerebral organoids (COs) produced from human-induced pluripotent stem cells (iPSCs). Under our experimental conditions, COs grow to form three-dimensional (3D) structures containing neural areas with cortical-like organization. Analysis of COs by histological and biochemical methods revealed that organoids produced from iPSCs derived from patients affected by familial AD or Down syndrome (DS) spontaneously develop over time pathological features of AD, including accumulation of structures highly reminiscent to amyloid plaques and neurofibrillary tangles. These pathological abnormalities were not observed in COs generated from various controls, including human iPSCs from healthy individuals, human iPSCs from patients affected by Creutzfeldt-Jakob disease, mouse embryonic stem cells (ESCs), or mouse iPSCs. These findings enable modeling genetic AD in a human cellular context in a 3D cortical-like tissue developed in vitro from patient-specific stem cells. This system provides a more relevant disease model compared to pre-existing methods and offers a new platform for discovery of novel targets and screening of drugs for therapeutic intervention.