Robots are complex systems, at the intersection of numerous engineering domains. The goal of many researchers is to build a fully capable and safe robot that can work and assist humans in their daily lives. To reach these goals, the complex robotic systems must be separated in different subsystem components such as perception, world understanding, navigation, manipulation, interfaces and interaction. These subsystems need to be safe and robust in order to synergistically work together. In particular, a reliable and general robot manipulation framework for free space and contact tasks is required for robots to become useful in new environments. In this thesis, we aim at developing a theoretical and practical foundation for safe and robust robotic manipulation, involving multiple simultaneous physical interactions with complex and unknown environments. We start with the well known operational space control framework: a task-oriented control methodology that enables task dynamic decoupling and hierarchical control structures. After reviewing the operational space control theory for controlling a robot task and posture, we present a series of practical considerations for its robust implementation on real hardware platforms. The integration in this framework of constraints such as joint limits and obstacles is then discussed, and a method to react safely to unexpected contacts on the robot structure during operations is proposed. These constraints are handled as control objectives in the control hierarchy, using artificial potential fields to generate repulsive forces and dynamically consistent projections to ensure an independent control of the constraints and task objectives. This systematic treatment of constraints at the control level enables a robust, autonomous execution of complex tasks in changing environments. This framework was extended over the years to consider underactuated robots in arbitrary contact situations. This resulted in a comprehensive formulation to the problem of controlling a high-dimensional robotic system involving complex tasks subject to various constraints, obstacles, balance and multiple contacts. Contacts are essential for robot manipulation. On the one hand, parts of the robot tasks involve physical interactions that need to be controlled precisely. On the other hand, further contacts are required on underactuated systems in order to enable the robot motion and guarantee its balance. In addition, contacts between the robot and the environment are subject to geometric and friction constraints that need to be addressed by the control framework. Therefore, in this thesis, the operational space whole-body control framework is completed to enable a systematic treatment of multi-contact scenarios. A virtual linkage model separates the contact forces into three sets. The resultant forces allow the robot to compensate for its underactuation. The task contact forces are controlled to their desired values. The internal forces provide a way to satisfy geometric and friction constraints. A method using barrier functions is proposed to specify a set of internal forces that ensure the robot's balance and contact stability. Even when the desired contact forces are correctly specified, their control remains a challenge. Indeed, the fast and discontinuous closed loop dynamics of stiff physical interactions leads to instabilities in robot force control. Therefore, we adapt a time domain passivity approach to guarantee the stability of explicit force controllers. This results in an increased robustness and safety for robotic systems in multiple contact scenarios. To develop effective interfaces for human-robot collaboration, we also study haptic robot teleoperation. Haptic devices provide an intuitive interface to remotely control robots and combine the high-level cognitive autonomy of humans with the autonomous manipulation capabilities of robots. The goal of haptic robot control is to maximize the transparency between the human operator and the robot environment. It means that the robot environment should be felt by the human as if they were directly interacting with it, and the human commands should be executed precisely by the robot. Transparency is very challenging to achieve when communication delays are present in the system, which occurs systematically when there is a significant physical distance between the controlled robot and its human operator. To address this challenge, we propose a new paradigm for performing haptic-robot control. Instead of relying on a global feedback loop, the new method establishes two autonomous controllers acting on the robot and the haptic device, interfaced via a dual-proxy model. The dual-proxy is a bridge between the local controllers. It generates appropriate motion and force inputs that are consistent with the task physical interactions. The model relies on the exchange of position, contact, and environment geometry information, avoiding the limitations caused by a direct force feedback between robot and haptic device in conventional teleoperation. To estimate the environment contact geometry in real-time, we also design a new perception algorithm that enables a fully autonomous implementation of the dual-proxy model. The performance of all the control methods presented in this thesis are evaluated via simulations and hardware experimental validation. Combining these methods together results in a robust, safe and generic manipulation control framework for complex robots in interaction with uncertain environments. Such framework is one of the key components for a complete and fully capable robotic system.