The self-consistency and empirical viability of standard semiclassical Einstein gravity (SSEG), viewed either as a fundamental theory or a mean-field approximation to some theory of quantum gravity, will be discussed. It will be shown that

1. SSEG, when viewed as a fundamental theory, is either not self-consistent or empirically ruled out (depending on how the matter side of the theory is interpreted); and
2. SSEG, when viewed as a mean-field approximation to a quantum gravity theory, has a domain of applicability that's much more limited than is widely assumed; and
3. the assumptions underlying the mean-field approximations in (2) are either physically inconsistent, ad hoc, or unrealistic.

It will then be shown that the aforementioned problems with the SSEG invalidate well-known applications of SSEG to astrophysics and cosmology; notably, Hawking's 1975 argument for black hole evaporation (and refinements thereof), the cosmological constant problem, arguments for the stability / instability of traversable wormholes and warp drive spacetimes, and cosmological perturbations in inflation. Historical context will be given throughout, including reference to the work of Moller and Rosenfeld in the 1960s, the subsequent work of the 70s and 80s on foundational issues in SSEG and renormalization/regularization techniques to make SSEG mathematically well-defined, the work of the 90's and 2000's on "stochastic gravity" (an extension of the of the SSEG), and work in the 2000s and 2010s connecting SSEG to "gravitational decoherence" proposals.