  Masses of the ground, orbitally and radially excited states of heavy-light
mesons are calculated within the framework of the QCD-motivated relativistic
quark model based on the quasipotential approach. Both light (q=u,d,s) and
heavy (Q=c,b) quarks are treated fully relativistically without application of
the heavy quark 1/m_Q expansion. The Regge trajectories in the (M^2, J) and
(M^2, n_r) planes are investigated and their parameters are obtained. The
results are in good agreement with available experimental data except for the
masses of the anomalous D^*_{s0}(2317), D_{s1}(2460) and D_{sJ}^*(2860) states.
