The technological processes that share the goal of combining dissimilar (III-V and Si) semiconductor materials on a single substrate in order to achieve enhanced performance and functionality of devices and circuits is reviewed. In particular, these techniques that enable monolithic solutions based on the fabrication of thin crystalline III-V films on a dissimilar substrate are addressed. This fabrication process can be completed by heteroepitaxial growth or thin-film transfer and the present state of these techniques is discussed. Here, III-V on Si is used as a generic example of heteroepitaxy and it is found that research is still largely focusing on the materials quality. However, creative materials engineering is displayed to assure a steady progress toward applicability. Thin-film transfer technology is currently tackling more processing related issues. It will be shown that heteroepitaxy is competing for some (large area) applications and that for other, often very appealing applications thin-film transfer is the only solution, offering high flexibility and exciting combinations of materials and functions. Besides these thin-film-based technologies, hybrid flip-chip is also a mature candidate for integration of optical and electronic functions.