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 P30 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 DJ(2550)0 and DJ∗(2600)0 are consistent with those of the 2S10(cu¯) and the 2S31(cu¯) states respectively, and the D1∗(2760)0, D3∗(2760)-, and DJ(2750)0 with those of the 1D31(cu¯), 1D33(dc¯), and 1D2(cu¯) states respectively. We tentatively identify the DJ∗(3000)0 as the 1F34(cu¯) and favor the DJ(3000)0 to be the 3S10(cu¯) although we do not rule out the 1F3 and 1F3′ assignment. For the recently observed charm-strange mesons we identify the Ds1∗(2709)±, Ds1∗(2860)-, and Ds3∗(2860)- as the 2S31(cs¯), 1D31(sc¯), and 1D33(sc¯) states respectively and suggest that the DsJ(3044)± is most likely the Ds1(2P1′) or Ds1(2P1) state although it might be the Ds2∗(2P32) 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.