The fundamental inaccessibility of the human neural cell types affected by neurological disorders prevents their isolation for in vitro studies of disease mechanisms or for drug screening efforts. Pluripotent stem cells represent a new interesting way to generate models of human neurological disorders, explore the physiopathological mechanisms and develop new therapeutic strategies. Disease-specific human embryonic stem cells were the first source of material to be used to study certain disease states. The recent demonstration that human somatic cells, such as fibroblasts or blood cells, can be genetically converted to induced pluripotent stem cells (hiPSCs) together with the continuous improvement of methods to differentiate these cells into disease-affected neuronal subtypes opens new perspectives to model and understand a large number of human pathologies. This review focuses on the opportunities concerning the use disease-specific human pluripotent stem cells as well as the different challenges that still need to be overcome. We also discuss the recent improvements in the genetic manipulation of human pluripotent stem cells and the consequences of these on disease modeling and drug screening for neurological diseases.