Computational protein design aims at identifying protein mutations and conformations with desired target properties (such as increased protein stability, switch of substrate specificity, or novel function) from a vast combinatorial space of candidate solutions. The development of algorithms to efficiently and accurately solve problems in protein design has thus posed significant computational and modeling challenges. Despite the inherent hardness of protein design, a number of computational techniques have been previously developed and applied to a wide range of protein design problems. In many cases, however, the available computational protein design techniques are deficient both in computational power and modeling accuracy. Typical simplifying modeling assumptions for computational protein design are the rigidity of the protein backbone and the discretization of the protein side-chain conformations. Here, we present the derivation, proofs of correctness and complexity, implementation, and application of novel algorithms for computational protein design that, unlike previous approaches, have provably-accurate guarantees even when backbone or continuous side-chain flexibility are incorporated into the model. We also describe novel divide-and-conquer and dynamic programming algorithms for improved computational efficiency that are shown to result in speed-ups of up to several orders of magnitude as compared to previously-available techniques. Our novel algorithms are further incorporated as part of K*, a provably-accurate ensemble-based algorithm for protein-ligand binding prediction and protein design. The application of our suite of protein design algorithms to a variety of problems, including enzyme redesign and small-molecule inhibitor design, is described. Experimental validation, performed by our collaborators, of a set of our computational predictions confirms the feasibility and usefulness of our novel algorithms for computational protein design.