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We prove a Berry-Esseen theorem and Edgeworth expansions for partial sums ofthe form $S_N=\sum_{n=1}^{N}f_n(X_n,X_{n+1})$, where $\{X_n\}$ is a uniformlyelliptic inhomogeneous Markov chain and $\{f_n\}$ is a sequence of uniformlybounded functions. The Berry-Esseen theorem holds without additionalassumptions, while expansions of order $1$ hold when $\{f_n\}$ is irreducible,which is an optimal condition.  For higher order expansions, we then focus on two situations. The first iswhen the essential supremum of $f_n$ is of order $O(n^{-\be})$ for some$\be\in(0,1/2)$. In this case it turns out that expansions of any order$r<\frac1{1-2\be}$ hold, and this condition is optimal. The second case isuniformly elliptic chains on a compact Riemannian manifold. When $f_n$ areuniformly Lipschitz continuous we show that $S_N$ admits expansions of allorders. When $f_n$ are uniformly H\"older continuous with some exponent$\al\in(0,1)$, we show that $S_N$ admits expansions of all orders$r<\frac{1+\al}{1-\al}$. For H\"older continues functions with $\al<1$ ourresults are new also for uniformly elliptic homogeneous Markov chains and asingle functional $f=f_n$. In fact, we show that the condition$r<\frac{1+\al}{1-\al}$ is optimal  even in the homogeneous case.

A Berry-Esseen theorem and Edgeworth expansions for uniformly elliptic inhomogeneous Markov chains