Extragalactic starbursts induced by gravitational interactions can now be studied from z = ~0 to ~2. The evidence that mergers of gas-rich galaxies tend to trigger galaxy-wide starbursts is strong, both statistically and in individual cases of major disk-disk mergers. Star formation rates appear enhanced by factors of a few to ~10^3 above normal. Detailed studies of nearby mergers and ULIRGs suggest that the main trigger for starbursts is the rapidly mounting pressure of the ISM in extended shock regions, rather than high- velocity, ~50 - 100 km/s cloud-cloud collisions. Numerical simulations demonstrate that in colliding galaxies the star formation rate depends not only on the gas density, but crucially also on energy dissipation in shocks. An often overlooked characteristic of merger-induced starbursts is that the spatial distribution of the enhanced star formation extends over large scales (~10 - 20 kpc). Thus, although most such starbursts do peak near the galactic centers, young stellar populations pervade merger remnants and explain why (1) age gradients in descendent galaxies are mild and (2) resultant cluster systems are far-flung. This review presents an overview of interesting phenomena observed in galaxy-wide starbursts and emphasizes that such events continue to accompany the birth of elliptical galaxies to the present epoch.