Lie algebroids appear throughout geometry and mathematical physics and realize the idea of a vector bundle whose sections have the structure of a Lie algebra. A classical result of A.~Vaintrob characterizes Lie algebroids and their morphisms in terms of a differential graded (dg-) manifolds, Z-graded versions of Q-manifolds, a.k.a. NQ-manifolds. The idea leads naturally to the notion of an L_\infty-algebroid. The situation with Lie bialgebroids and their morphisms is more complicated, as bialgebroids combine covariant and contravariant features. We approach Lie and L_\infty-bialgebroids in terms of symplectic dg-manifolds (a.k.a. NQP-manifolds) and integrable odd Hamiltonians, building on the work of Dmitry Roytenberg. We also discuss the notions of morphisms of dg-manifolds and L_\infty-bialgebroids. This is a joint work with Denis Bashkirov.