  We introduce and consider the inner-model reflection principle, which asserts
that whenever a statement $\varphi(a)$ in the first-order language of set
theory is true in the set-theoretic universe $V$, then it is also true in a
proper inner model $W\subsetneq V$. A stronger principle, the ground-model
reflection principle, asserts that any such $\varphi(a)$ true in $V$ is also
true in some non-trivial ground model of the universe with respect to set
forcing. These principles each express a form of width reflection in contrast
to the usual height reflection of the L\'evy-Montague reflection theorem. They
are each equiconsistent with ZFC and indeed $\Pi_2$-conservative over ZFC,
being forceable by class forcing while preserving any desired rank-initial
segment of the universe. Furthermore, the inner-model reflection principle is a
consequence of the existence of sufficient large cardinals, and lightface
formulations of the reflection principles follow from the maximality principle
MP and from the inner-model hypothesis IMH. We also consider some questions
concerning the expressibility of the principles.
