  The masses of the heavy tetraquarks with open charm and bottom are calculated
within the diquark-antidiquark picture in the framework of the relativistic
quark model. The dynamics of the light quarks and diquarks is treated
completely relativistically. The diquark structure is taken into account by
calculating the diquark-gluon form factor. New experimental data on charmed and
charmed-strange mesons are discussed. Our results indicate that the anomalous
scalar D_{s0}^*(2317) and axial vector D_{s1}(2460) mesons could not be
considered as diquark-antidiquark bound states. On the other hand, D_s(2632)
and D_{sJ}^*(2860) could be interpreted as scalar and tensor tetraquarks,
respectively. The predictions for masses of the corresponding bottom
counterparts of the charmed tetraquarks are given.
