Object transport is a major application of robots in logistics and manufacturing automation. In the long-standing effort to optimize operations, robot throwing introduces a new paradigm, offering unprecedented dexterity and efficiency. Yet, existing solutions are limited by narrow operating conditions (restricted postures and object sets), reliance on data-driven black-box models, and sample-intensive learning, all of which hinder scalability and deployment.

To address these challenges, this thesis conducts a systematic study of robot throwing, vertically integrating modeling, planning, and learning. The focus is on the discovery and utilization of graceful computational and physical structures, which enable reliable algorithms and robust performance. Specifically, four major contributions are presented: (1) Fast and adaptive throwing: Leveraging the separability of the nonconvex feasibility problem, we develop the first real-time planning algorithm for dexterous throwing. Offline, kinematic analysis generates a dictionary of feasible configurations tailored to the robot's geometry and actuation limits. Online, candidate queries and filtering quickly yield diverse feasible throws, enabling reactive replanning to sustain high task efficiency in dynamic environments. (2) Robust dexterous throwing under release uncertainty: Release uncertainty causes different landing outcomes for identical throwing motions. By abstracting release dynamics with a kinematic surrogate release delay model and leveraging the throwing goal manifold, we formulate a motion-planning scheme robust against release uncertainty. A convex relaxation exploiting the quasi-linearity of the goal manifold achieves bounded error and real-time solving. This enables the throwing of diverse (including deformable) objects without prior knowledge or real-data training. (3) Physical modeling of transient release dynamics: The transient phase of vanishing grasping force during release significantly affects the object's landing pose (position and orientation) and is not well understood. We show that the existing modeling strategy, which combines rigid-body dynamics with patch-friction models, is highly sensitive and inaccurate. To address this, we propose a physical model of release dynamics based on the dominant in-hand spinning during the transient. Model validation under a wide range of throwing conditions demonstrates that its accuracy is on par with end-to-end data-driven models trained on massive datasets. (4) Learning to throw-flip with a desired landing pose: Revolute-arm throws suffer from parasitic end-effector rotation, limiting achievable landing poses. Using the impulse-momentum principle, we exploit the temporal hinge effect during release to decouple linear and angular motion, greatly enlarging the feasible landing-pose space. To bridge the gap between limited model-based planning and costly end-to-end learning, we design an adaptive framework that assimilates empirical data with projectile dynamics, significantly reducing sample complexity.

By integrating theoretical advancements with extensive experimental validation, this thesis provides a substantial computational and physical understanding of robot throwing. The resulting algorithms advance the technology readiness level (TRL) of robot throwing across multiple dimensions, laying the foundation for scalable and ubiquitous throwing robots.