Epitaxial integration of III–V optical functionalities on silicon (Si) is the key to complement current Si photonics, facilitating the development of scalable, compact photonic integrated circuits. Here we aim to outline this field, focusing on the III–V semiconductor materials and the III–V lasers grown on Si. This paper is divided into two main parts: in the first part, we discuss III–V materials grown on Si, including the low-index {hhl} facets, (001) Si surface and anti-phase boundary, and dislocation engineering. The second part centres at III–V lasers grown on Si: we will first discuss III–V lasers that are highly tolerant to dislocations, including quantum dot/dash diode lasers, interband cascade, and quantum cascade lasers grown on Si from near infrared to long-wave infrared. We then move to the selective heteroepitaxy of low dislocation density III–Vs for the bufferless lasers. Finally, we review the III–V nanowire photonic crystal lasers grown on Si, which offers a different approach to overcome material mismatch and grow dislocation free III–V structures on silicon. We start with briefly introducing the recent progress of each technology, followed with a discussion of its key advantages, research challenge and opportunities.