Cerebral (or brain) organoids derived from human cells have enormous potential as physiologically relevant downscaled models of the human brain. In fact, these stem cell-derived neural aggregates resemble the three-dimensional (3D) cytoarchitectural arrangement of the brain overcoming not only the unrealistic somatic flatness but also the planar neuritic outgrowth of the two-dimensional (2D) cultures. Despite the growing use of cerebral organoids in scientific research, a more critical evaluation of their reliability and reproducibility in terms of cellular diversity, mature traits, and neuronal dynamics is still required. Specifically, a quantitative framework for generating and investigating these models of the human brain is lacking. To this end, the aim of this review is to inspire new computational and technology driven ideas for methodological improvements and novel applications of brain organoids. After an overview of the organoid generation protocols described in the literature, we review the computational models employed to assess their formation, organization and resource uptake. The experimental approaches currently provided to structurally and functionally characterize brain organoid networks for studying single neuron morphology and their connections at cellular and sub-cellular resolution are also discussed. Well-established techniques based on current/voltage clamp, optogenetics, calcium imaging, and Micro-Electrode Arrays (MEAs) are proposed for monitoring intra- and extra-cellular responses underlying neuronal dynamics and functional connections. Finally, we consider critical aspects of the established procedures and the physiological limitations of these models, suggesting how a complement of engineering tools could improve the current approaches and their applications.