In this paper, we deal with optical Airy beams propagating in a nonlinear photorefractive crystal. We first study the dynamics of one Airy beam and show that it evolves in two stages: when we apply a focusing nonlinearity on the crystal, the output beam first turns into an off-shooting soliton. Then we observe a relaxation-type dynamics towards a focused redistributed solution where an Airy-like profile and the previous off-shooting soliton are superimposed. In a second step we add a second Airy beam counterpropagating in the nonlinear crystal. We show that the interactions induced by counter-propagating Airy beams allow for achieving complex waveguiding structures that would otherwise require the counter-propagating interactions of more than two Gaussian beams. Finally we present that the stationary waveguide structures shown previously can be switched to spatiotemporally varying structures by tuning the photorefractive nonlinearity of the system. The system dynamically evolves from a steady-state regime to time-dependent stable and turbulent states where the off-shooting solitons begin to move first periodically then erratically around specific Airy-induced output positions. These localized spatiotemporal dynamics are induced by the peculiar energy distribution of the counterpropagating Airy beams.