text: Several quasi-2-D systems, including layered transition metal dichalcogenides, undergo Peierls transitions to form quasi-2-D CDWs. These result from multiple nesting wavevectors coupling different flat regions of the Fermi surface. The charge modulation can either form a honeycomb lattice with hexagonal symmetry or a checkerboard pattern. A concomitant periodic lattice displacement accompanies the CDW and has been directly observed in 1T-TaS using cryogenic electron microscopy. In 2012, evidence for competing, incipient CDW phases were reported for layered cuprate high-temperature superconductors such as YBCO.