We suggest that the mass lost during the evolution of very massive stars may be dominated by optically thick, continuum-driven outbursts or explosions, instead of by steady line-driven winds. In order for a massive star to become a WR star, it must shed its H envelope, but new estimates of the effects of clumping in winds indicate that line driving is vastly insufficient. We discuss massive stars above roughly 40-50 Msun, for which the best alternative is mass loss during brief eruptions of luminous blue variables (LBVs). Our clearest example of this phenomenon is the 19th century outburst of eta Car, when the star shed 12-20 Msun or more in less than a decade. Other examples are circumstellar nebulae of LBVs, extragalactic eta Car analogs (``supernova impostors''), and massive shells around SNe and GRBs. We do not yet fully understand what triggers LBV outbursts, but they occur nonetheless, and present a fundamental mystery in stellar astrophysics. Since line opacity from metals becomes too saturated, the extreme mass loss probably arises from a continuum-driven wind or a hydrodynamic explosion, both of which are insensitive to metallicity. As such, eruptive mass loss could have played a pivotal role in the evolution and fate of massive metal-poor stars in the early universe. If they occur in these Population III stars, such eruptions would profoundly affect the chemical yield and types of remnants from early SNe and hypernovae.
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