In this article, the concepts of handedness and negative material parameters are analyzed at a general and qualitative level. Three different usages of handedness in metamaterials and electromagnetics are distinguished: left-handedness as characterization of double-negative materials, handedness of the polarization of a plane wave, and chirality in the structure of matter. The symmetry of the treatment between left and right is discussed from the point of view of the three uses of the handedness. It is essential to distinguish the helicity of the spatial shape of the field vector as opposed to the temporal behavior of the field at a given position in space. Negative refraction and backward-wave characteristics are discussed in the case when structural chirality of the medium splits the wave numbers of the eigenwaves. Finally, negative refraction is connected with anisotropic and bi-anisotropic materials.