Given the state of a system is not completely observable, filtering is concerned with state estimation based on partial observations of the system state. It enjoys many applications in the control of partially observed systems, target tracking, signal processing, statistics, and financial engineering. Devoted to the conditional distribution or density, the celebrated results of the Kushner equation and Duncan-Mortensen-Zakai equation produce nonparametric estimations of the conditional distribution/density. Approximating their solutions will suffer the curse of dimensionality. In this talk, we first introduce a new filtering algorithm termed deep filtering based on the deep learning framework. Instead of approximating the conditional distribution or density, we focus on state estimation or conditional mean. We convert the filtering problem to an optimization problem by finding the optimal weights of a deep neural network (DNN). This solves a long-standing (60-year-old) challenging problem in computational nonlinear filtering and has the potential to overcome the curse of dimensionality. Then, we present our work on deep filtering with adaptive learning rates. Besides updating the parameters of the DNN, we also update the learning rates adaptively. Our algorithm is a two-time-scale stochastic gradient descent algorithm. The updating of the learning rates is unsupervised learning. We proved the asymptotic results of our algorithm and achieved error bounds for the parameters of the neural network. Finally, we will present some numerical examples to show the efficiency and robustness of our algorithm. This is based on joint work with Prof. George Yin and Prof. Qing Zhang.