While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively-weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss 1) the development of the energy landscape theory of biomolecular folding, 2) recent advances towards establishing a consistent understanding of folding and function, and 3) emerging themes in the functional motions of enzymes, biomolecular motors, and other biomolecular machines. Recent theoretical, computational, and experimental lines of investigation are providing a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provide significant contributions to the free-energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.