Charge density waves (CDW) are an emergent periodic modulation of the electron density that permeates crystals with strong electron-lattice coupling. TaS:2: and TaSe:x:S:2-x: host several charge density wave states that spontaneously break crystal symmetries, mediate metal-insulator transitions, and compete with superconductivity. These quantum states are promising candidates for novel devices, efficient ultrafast nonvolatile switching, and suggest elusive chiral superconductivity.