AKSZ sigma models are physical models constructed from dg manifolds (Q-manifolds). One of important AKSZ sigma models is the Poisson sigma model, which gives the Kontsevich formula in the deformation quantization and the formality by the quantization. We present generalizations of AKSZ sigma models as classical field theories, higher dimensional generalizations and deformations by pre-multisymplectic forms called 'fluxes'. Geometric structures of these theories including dg structures induced from BV formalisms are described by geometry of Lie algebroids and higher algebroids. We discuss problems of quantizations of AKSZ sigma models and generalized theories.