Microglia play a role in the emergence and preservation of a healthy brain microenvironment. Dysfunction of microglia has been associated with neurodevelopmental and neurodegenerative disorders. Investigating the function of human microglia in health and disease has been challenging due to the limited models of the human brain available. Here, we develop a method to generate functional microglia in human cortical organoids (hCOs) from human embryonic stem cells (hESCs). We apply this system to study the role of microglia during inflammation induced by amyloid-β (Aβ). The overexpression of the myeloid-specific transcription factor PU.1 generates microglia-like cells in hCOs, producing mhCOs (microglia-containing hCOs), that we engraft in the mouse brain. Single-cell transcriptomics reveals that mhCOs acquire a microglia cell cluster with an intact complement and chemokine system. Functionally, microglia in mhCOs protect parenchyma from cellular and molecular damage caused by Aβ. Furthermore, in mhCOs, we observed reduced expression of Aβ-induced expression of genes associated with apoptosis, ferroptosis, and Alzheimer's disease (AD) stage III. Finally, we assess the function of AD-associated genes highly expressed in microglia in response to Aβ using pooled CRISPRi coupled with single-cell RNA sequencing in mhCOs. In summary, we provide a protocol to generate mhCOs that can be used in fundamental and translational studies as a model to investigate the role of microglia in neurodevelopmental and neurodegenerative disorders.