Modeling and control of dynamical systems are fundamental problems across several scientific and engineering disciplines. Traditionally, dynamical systems or processes are modeled with a set of differential equations constructed based on physical principles and extensive experiments by human experts. However, in many practical scenarios, analytical modeling is very challenging and/or can only describe the system behavior partially. Furthermore, real-world dynamical processes are inherently nonlinear which makes the downstream task of control notoriously difficult. In recent years, the success of deep learning in various complex tasks has motivated many researchers to exploit deep learning for automatic modeling and control synthesis for dynamical systems from data. However, deep learning methods have their own drawbacks, for example, high sample complexity, requirements of regular data structure/sampling, difficulty in long-term prediction, lack of generalizability outside of training scenarios, etc. This thesis presents a collection of deep learning frameworks for data-driven modeling and control of dynamical systems addressing the aforementioned challenges. One branch of this dissertation focuses on the prediction problem as an independent task. Knowledge-incorporated deep modeling frameworks are proposed for better generalization and long-term prediction of multi-agent and spatiotemporal dynamics. Additionally, a deep learning framework is developed for learning prediction models for spatiotemporal processes using data collected from sparsely and irregularly distributed data sites. The other branch of this thesis focuses on learning control policies for nonlinear dynamical systems using DNNs. A novel method for nonlinear control design coupling deep learning with control theory is introduced. The proposed learning method is evaluated in simulation for unknown systems by means of partial system identification. Moreover, the proposed approach is experimentally verified to control a real robot with a known nominal model. The same learning approach is further evaluated to learn control for high-dimensional systems by means of data-driven deep model order reduction.