Let χl(G),χl′ (G),χl′′ (G), and Δ(G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. (1) 2 ≤χl(G) ≤ 3 andχl (G) = 2 if and only if G is bipartite with at most one cycle. (2)Δ(G) ≤χl′(G) ≤Δ(G) + 1 andχl′ (G) =Δ(G) + 1 if and only if G is an odd cycle. This proves the well-known list edge coloring conjecture for outerplane graphs. (3)χl′′(G) =Δ(G) + 1 if Δ(G) ≥ 4 and χl′′(G) ≤ 5 if Δ(G) ≤ 3. This proves a conjecture of O. V. Borodin, A. V. Kostochka and D. R. Woodall, List edge and list total coloring of multigraphs, J. Comb. Theory B, 71 (1997), 184–204 for outerplane graphs.