Heavy-light and heavy-heavy mesons from lattice QCD

I discuss a recent lattice QCD computation of the low-lying spectra of D mesons, D_s mesons and charmonium states with total angular momentum J = 0, 1, 2, parity -, + and charge conjugation -, +. The results are extrapolated to physically light u/d quark masses and to the continuum. All error sources are investigated and quantified including finite volume corrections and effects due to isospin breaking such that a direct comparison to available experimental results is possible in a meaningful way. I also outline, how to study more complicated mesonic systems, which have a heavy-heavy-light-light four-quark structure, using lattice QCD, and present corresponding preliminary results.