Neurological disorders have emerged as a predominant healthcare concern in recent years due to their severe consequences on quality of life and prevalence throughout the world. Understanding the underlying mechanisms of these diseases and the interactions between different brain cell types is essential for the development of new therapeutics. Induced pluripotent stem cells (iPSCs) are invaluable tools for neurological disease modeling, as they have unlimited self-renewal and differentiation capacity. Mounting evidence shows: 1) various brain cells can be generated from iPSCs in 2-dimensional (2D) monolayer cultures; 2) further advances in 3D culture systems have led to the differentiation of iPSCs into organoids with multiple brain cell types and specific brain regions. These 3D organoids have gained widespread attention as in vitro tools to recapitulate complex features of the brain, and 3) Complex interactions between iPSC-derived brain cell types can recapitulate physiological and pathological conditions of blood-brain barrier (BBB). As iPSCs can be generated from diverse patient populations, researchers have effectively applied 2D, 3D and BBB models to recapitulate genetically complex neurological disorders and reveal novel insights into molecular and genetic mechanisms of neurological disorders. In this review, we describe recent progress in the generation of 2D, 3D and BBB models from iPSCs and further discuss their limitations, advantages, and future ventures. This review also covers the current status of applications of 2D, 3D and BBB models in drug screening, precision medicine, and modeling a wide range of neurological diseases (e.g., neurodegenerative diseases, neurodevelopmental disorders, brain injury, and neuropsychiatric disorders).