Human pluripotent stem cell (hPSC)-derived neuron cultures have emerged as models of electrical activity in the human brain. Microelectrode arrays (MEAs) measure changes in the extracellular electric potential of cell cultures or tissues and enable the recording of neuronal network activity. MEAs have been applied to both human subjects and hPSC-derived brain models. Here, we review the literature on the functional characterization of hPSC-derived two- and three-dimensional brain models with MEAs and examine their network function in physiological and pathological contexts. We also summarize MEA results from the human brain and compare them to the literature on MEA recordings of hPSC-derived brain models. MEA recordings have shown network activity in two-dimensional hPSC-derived brain models that is comparable to the human brain and revealed pathology-associated changes in disease models. Three-dimensional hPSC-derived models such as brain organoids possess a more relevant microenvironment, tissue architecture and potential for modeling the network activity with more complexity than two-dimensional models. hPSC-derived brain models recapitulate many aspects of network function in the human brain and provide valid disease models, but certain advancements in differentiation methods, bioengineering and available MEA technology are needed for these approaches to reach their full potential.