We calculate the properties of excited charm and charm-strange mesons. We use the relativized quark model to calculate their masses and wave functions that are used to calculate radiative transition partial widths and the P-3(0) quark-pair-creation model to calculate their strong decay widths. We use these results to make quark model spectroscopic assignments for recently observed charm and charm-strange mesons. In particular, we find that the properties of the D-J(2550)(0) and D-J*(2600)(0) are consistent with those of the 2(1)S(0)(c (u) over bar) and the 2(3)S(1)(c (u) over bar) states respectively, and the D-1*(2760)(0), D-3*(2760)(-), and D-J(2750)(0) with those of the 1(3)D(1)(c (u) over bar), 1(3)D(3)d(d (c) over bar), and 1D(2)(c (u) over bar) states respectively. We tentatively identify the D-J*(3000)(0) as the 1(3)F(4)(c (u) over bar) and favor the D-J(3000)(0) to be the 3(1)S(0)(c (u) over bar) although we do not rule out the 1F(3) and 1F'(3) assignment. For the recently observed charm-strange mesons we identify the D-s1*(2709)(+/-), D-s1*(2860)(-), and D-s3*(2860)(-) as the 2(3)S(1)(c (s) over bar), 1(3)D(1)(s (c) over bar), and 1(3)D(3)(s (c) over bar) states respectively and suggest that the D-sJ(3044)(+/-) is most likely the D-s1(2P'(1)) or D-s1(2P(1)) state although it might be the D-s2*(2(3)P(2)) with the DK final state too small to be observed with current statistics. Based on the predicted properties of excited states, that they do not have too large a total width and that they have a reasonable branching ratio to simple final states, we suggest states that should be able to be found in the near future. We expect that the tables of properties summarizing our results will be useful for interpreting future observations of charm and charm-strange mesons.