This paper is a review of recent advances in studies of the magnetic, electronic, spintronic, and phononic properties of chiral crystals, with a focus on the connection between the Dzyaloshinskii-Moriya interaction (DMI) and chirality in materials. Importantly, a microscopic DMI is elevated to a macroscopic Lifshitz invariant (LI) in chiral crystals, where mirror reflection and inversion symmetry are globally broken. As a consequence, chiral crystals exhibit nontrivial physical responses over a macroscopic scale. Indeed, in chiral magnetism, a chiral spin soliton lattice (CSL) appears in monoaxial chiral magnetic crystals and exhibits various nontrivial physical properties characterized by the coherent and topological nature of the CSL. This CSL isone of the prominent outcomes arising from the DMI and LI, as envisioned by Dzyaloshinskii in the 1960s. Furthermore, a giant spin polarization emerges over a macroscopic scale in a wide range of chiral materials from organic molecules to inorganic crystals. The first-order spatial dispersion, such as the LI, also appears in elastic or phonon degrees of freedom in chiral crystals. These examples show how a time-even pseudoscalar term, which corresponds to a generalized concept of the DMI and LI, is realized in chiral media.