The brain is our most complex and least understood organ. Animal models have long been the most versatile tools available to dissect brain form and function; however, the human brain is highly distinct from that of standard model organisms. In addition to existing models, access to human brain cells and tissues is essential to reach new frontiers in our understanding of the human brain and how to intervene therapeutically in the face of disease or injury. In this review, we discuss current and developing culture models of human neural tissue, outlining advantages over animal models and key challenges that remain to be overcome. Our principal focus is on advances in engineering neural cells and tissue constructs from human pluripotent stem cells (PSCs), though primary human cell and slice culture are also discussed. By highlighting studies that combine animal models and human neural cell culture techniques, we endeavor to demonstrate that clever use of these orthogonal model systems produces more reproducible, physiological, and clinically relevant data than either approach alone. We provide examples across a range of topics in neuroscience research including brain development, injury, and cancer, neurodegenerative diseases, and psychiatric conditions. Finally, as testing of PSC-derived neurons for cell replacement therapy progresses, we touch on the advancements that are needed to make this a clinical mainstay.