  We establish Cram\'er-type moderate deviation theorems for sums of locally
dependent random variables and combinatorial central limit theorems. Under some
mild exponential moment conditions, optimal error bounds and convergence ranges
are obtained. Our main results are more general or shaper than the existing
results in the literature. The main results follows from a more general
Cram\'er-type moderate deviation theorem for dependent random variables without
any boundedness assumptions, which is of independent interest. The proofs
couple Stein's method with a recursive argument.
