For millennia, people have designed diverse machines to perform countless different tasks. \textit{Design} -- the creation of a system according to a \textit{rational plan}, is so ubiquitous in the engineering of mechanical systems, that the word became synonymous with the final engineered product. However, recent advances in neuroscience and computer science suggest a different approach to constructing mechanical systems, namely \textit{learning}. If a system can modify the properties of its components in response to external inputs, it may be able to learn desired behaviors by observing examples of use. Learning mechanical systems may have distinct advantages over designed systems, such as the potential to be trained for a task by an end-user rather than a designer, and the ability to adapt to new tasks while still capable of accomplishing previously established ones. In this work, we study and compare design and learning approaches in two types of mechanical systems, self-folding origami and elastic networks. By utilizing an energy-based viewpoint, we show how these systems are designed to perform certain tasks (e.g. folding in a desired way, or having predefined multi-stability), and how they can learn to perform such tasks by experiencing examples of use. We elucidate the distinct advantages and disadvantages of design and learning approaches in these specific systems. Finally, we lay out explicit analogies between learning mechanical systems and learning in neuroscience and computer science. Thus, we hope that future mechanical engineering disciplines will exploit the surge in learning theory to create new classes of learning machines, capable of feats yet impervious to traditional design frameworks.