The Laser Floating Zone (LFZ) technique, also known as Laser-Heated Pedestal Growth (LHPG), has been developed throughout the last several decades as a simple, fast, and crucible-free method for growing high-crystalline-quality materials, particularly when compared to the more conventional Verneuil, Bridgman-Stockbarger, and Czochralski methods. Multiple worldwide efforts have, over the years, enabled the growth of highly oriented polycrystalline and single-crystal high-melting materials. This work attempted to critically review the most representative advancements in LFZ apparatus and experimental parameters that enable the growth of high-quality polycrystalline materials and single crystals, along with the most commonly produced materials and their relevant physical properties. Emphasis will be given to materials for photonics and optics, as well as for electrical applications, particularly superconducting and thermoelectric materials, and to the growth of metastable phases. Concomitantly, an analysis was carried out on how LFZ may contribute to further understanding equilibrium vs. non-equilibrium phase selectivity, as well as its potential to achieve or contribute to future developments in the growth of crystals for emerging applications.