Nanometer-scale crystals of bulk group IV, III-V, II-VI, IV-VI, I-III-VI2, and metal-halide perovskite semiconductors, dispersed in solvents, are known as colloidal nanocrystals and form an excellent, solution-processable materials class for thin film and flexible electronics. This review surveys the size, composition, and surface chemistry-dependent properties of semiconductor NCs and thin films derived therefrom and provides physico-chemical insight into the recent leaps forward in the performance of NC field-effect transistors. Device design and fabrication methods are described that have enabled the demonstration and scaling up in complexity and area and scaling down in device size of flexible, colloidal nanocrystal integrated circuits. Finally, taking stock of the advances made in the science and engineering of NC systems, challenges and opportunities are presented to develop next-generation, colloidal NC electronic materials and devices, important to their potential in future computational and in Internet of Things applications.