Surrogate models are often constructed to speed up the computational procedure of the Bayesian inverse problems(BIPs), as the forward models can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear concentration of the posterior, traditional surrogate approaches are still not feasible for large scale problems. This talk will survey our recent works in designing surrogate models using deep learning techniques. Several fast and efficient algorithms based on deep neural networks(DNN) to solve BIPs will be covered, including adaptive multi-fidelity surrogate modeling and local approximations. Numerical examples are presented to confirm that new approaches can obtain accurate posterior information with a limited number of forward simulations.