The pharmaceutical industry is continuing to face high research and development (R&D) costs and low overall success rates of clinical compounds during drug development. There is an increasing demand for development and validation of healthy or disease-relevant and physiological human cellular models that can be implemented in early-stage discovery, thereby shifting attrition of future therapeutics to a point in discovery at which the costs are significantly lower. There needs to be a paradigm shift in the early drug discovery phase (which is lengthy and costly), away from simplistic cellular models that show an inability to effectively and efficiently reproduce healthy or human disease-relevant states to steer target and compound selection for safety, pharmacology, and efficacy questions. This perspective article covers the various stages of early drug discovery from target identification (ID) and validation to the hit/lead discovery phase, lead optimization, and preclinical safety. We outline key aspects that should be considered when developing, qualifying, and implementing complex in vitro models (CIVMs) during these phases, because criteria such as cell types (e.g., cell lines, primary cells, stem cells, and tissue), platform (e.g., spheroids, scaffolds or hydrogels, organoids, microphysiological systems, and bioprinting), throughput, automation, and single and multiplexing endpoints will vary. The article emphasizes the need to adequately qualify these CIVMs such that they are suitable for various applications (e.g., context of use) of drug discovery and translational research. The article ends looking to the future, in which there is an increase in combining computational modeling, artificial intelligence and machine learning (AI/ML), and CIVMs.