The fundamental objective of robotics is to enhance the productivity of humans while interacting in potentially unstructured environments. In this sense, Human-centered robots must be fast, stable, and robust when performing varied and complicated tasks during mission execution. Although industrial robots have seen some advancements regarding motion planning and control, they are largely limited to simple pre-defined tasks in structured environments. However, to achieve highly dynamic motions for dexterous manipulation or agile locomotion in complex robots, we need to consider the use of nonlinear dynamics, complex constraints, multiple contacts, disturbances, and uncertainties. These are fundamental requirements needed to advance the use of general purpose robots dynamically interacting in a wider variety of environments. Therefore, this thesis addresses challenges that arise from the employment of optimization techniques and sophisticated realtime algorithms for the control and deployment of realistic and practical robots in human environments. Considering the above challenges, we propose efficient trajectory generation and trajectory tracking methods as the next paradigms for whole-body control (WBC). First, we formulate a class of motion planning problems to directly obtain dynamically feasible state trajectories in multi-contact robots and the corresponding control inputs. Typically, it takes a tremendous amount of time to solve the end-to-end trajectory generation problem using large-scale standard Nonlinear Programming (NLP). We propose a new sampling-based method together with a Partially Observable Markov Decision Process to break down the trajectory generation problem into tractable parts. In doing so, the number of decision variables is drastically reduced. As a result, we solve the optimization problem much faster than using existing NLP techniques. In addition, we incorporate reachability analysis tools for determining whether the planned trajectories are reachable and discard unfeasible trajectories during optimization. Because simplified models are frequently utilized in locomotion studies to generate walking patterns, planned contact locations may not be feasible due to model mismatch and robot constraints. In contrast, our method enables the generation of dynamically feasible trajectories to reach planned contact location considering full-body dynamics and realistic constraints. The proposed methods are applied to contact constrained manipulation and bipedal locomotion problems to enhance capabilities of robots maneuvering in complex environments without slip or loss of balance. Second, we explore the fundamentals of WBC and use this insight to push forward the capabilities of WBC approaches. One of the problems we explore is the verification of stability of legged robots under unknown external perturbations. In such cases, the closed-loop control system controlled by WBC approaches may become unstable if external perturbations are not properly analyzed with stability verification. To verify stability, we leverage the so-called Centroidal Dynamics of legged robots and a type of WBC dubbed Whole-Body Locomotion Control (WBLC). Using a feedback-linearized state-space model, we obtain appropriate feedback gains for WBC to make our robot stable and robust under perturbations. Another challenge of WBC stems from the reliance on classical feedback control theory. Classical PD control is unsuitable for a noisy system, therefore WBC cannot be directly applied to stochastic systems. Classical WBC approaches do not consider the covariance of the terminal states as constraints which is a more efficient way to control robots with precision. We propose a new control approach, called Hierarchical Covariance Control (HCC) to enforce covariance constraints. Our proposed HCC is a stochastic version of WBC to decrease task errors when uncertainty is substantial. The last improvement I explore regarding WBC is the employment of Model Predictive Control (MPC) instead of solving an instantaneous optimization problem, which cannot guarantee global optimality. As such, we consider longer receding time horizons for MPC, thus improving the tracking performance by reducing the accumulated error norm while executing hierarchical tasks. Overall, our research focuses on the end-to-end process spanning trajectory planning to feedback control enabling the generating of multi-contact and constrained dynamic motions of complex robots operating in realistic setups. The various contributions of this thesis are in the areas of computational efficiency for whole-body trajectory generation, robustness of WBC control algorithms, and significant improvements in trajectory tracking using WBC algorithms. We verify the proposed approaches both in simulations and real experiments using various robotic systems