A body is defined as chiral if it cannot be superimposed on its mirror image by any rigid-body motion. Chirality, the property of being chiral, can be generalized from physical objects to flows and fields. It is a unifying concept in science, encompassing physics, topology, geometry, chemistry and biology. An associated notion, handedness, assigns a sign to a chiral body, positive for a right-handed structure, and negative for a left-handed structure. Despite their natural and intuitive nature, both chirality and handedness are surprisingly hard to quantify, and multiple geometric measures can be assigned for the same body. From a physical perspective, chirality becomes relevant when its presence manifests itself through experimentally observable effects. In particular, the physical approach to chirality is to define it through the interaction of a body with external fields. For instance, a chiral rigid body subject to an orienting field may rotate, and chirality can then be characterized mathematically in terms of the spectral properties of a pseudotensor connecting this rotation to the global field. While this approach is suitable for nondeformable bodies, many natural systems are intrinsically soft: when exposed to external loads or fields, they not only change their orientation but also their shape, and this deformation itself may exhibit chirality. For instance, the deformation path of the end point of a helical spring during extension is itself chiral, where the handedness reflects both geometric helical handedness and material properties. Understanding the contributions of geometry, material properties, and external fields in the chiral behavior of physical systems is the central question addressed here. We first review the history of chirality and its central place in the evolution of physical, chemical, and biological theories. Second, we introduce different notions of chirality attached to bodies or fields. Third, we consider and quantify hard chirality, defined as the physical chirality of rigid structures in orienting fields. Fourth, we develop a theory of soft chirality for soft bodies by assigning pseudotensors to deformations, thereby linking microscopic constitutive properties to emergent macroscopic responses.