There is currently much activity toward the integration of mid-infrared semiconductor lasers on Si substrates for developing a variety of smart, compact, sensors based on Si-photonics integrated circuits. We review this rapidlyevolving research field, focusing on the epitaxial integration of antimonide lasers, the only technology covering the whole mid-to-far-infrared spectral range. We explain how a dedicated molecular-beam epitaxy strategy allows for achieving high-performance GaSb-based diode lasers, InAs/AlSb quantum cascade lasers, and InAs/GaInSb interband cascade lasers by direct growth on on-axis (001)Si substrates, whereas GaAs-on-Si or GaSb-on-Si layers grown by metal-organic vapor phase epitaxy in large capability epitaxy tools are suitable templates for antimonide laser overgrowth. We also show that etching the facets of antimonide lasers grown on Si is a viable approach in view of photonic integrated circuits. Remarkably, this review shows that while diode lasers are sensitive to residual crystal defects, the quantum cascade and interband cascade lasers grown on Si exhibit performances comparable to those of similar devices grown on their native substrates, due to their particular band structures and radiative recombination channels. Long device lifetimes have been extrapolated for interband cascade lasers. Finally, routes to be further explored are also presented.