Brain-on-a-chip (BOC) refers to a miniaturized in vitro platform that integrates living neuronal networks on a micro-engineered chip, enabling the simulation of brain functions, neural activities and physiological responses. BOC technology is an advanced evolution of microphysiological systems (MPS) and Lab-on-a-Chip platforms, providing novel paradigms for in vitro modeling and exploring early-stage biocomputing by interfacing living neural networks with engineered electronics. Microelectrode arrays (MEAs) serve as the critical physical interface for bidirectional communication in these systems. In this review, we systematically examine the technological landscape and engineering requirements of MEAs tailored for BOC applications, evaluating them across electrical characteristics, structural properties, and biocompatibility. Two primary classes of current MEA technologies, including planar arrays for 2D neural cultures and 3D flexible arrays for brain organoids, are discussed in detail. We highlight the transition from passive planar electrodes to high-density active CMOS and TFT-based arrays, and detail how 3D flexible MEAs utilize endogenous integration and exogenous wrapping strategies to overcome tissue-mechanics mismatches. Furthermore, the integration of MEAs with microfluidics, optoelectronics, and electrochemical sensors to enable multimodal monitoring is explored. With the advantages of the various MEAs, the application of MEAs for BOC, particularly in biological computing and network plasticity research, is discussed. Finally, future technological developments in scalability bottlenecks, chronic stability, and the incorporation of artificial intelligence for MEAs of BOC are prospected.