In the last few decades, chalcogenide glasses have received considerable attention as infrared-transmitting materials for infrared systems such as surveillance cameras. In this review, two chalcogenide glass groups are introduced, where germanium sulfide and gallium sulfide are used as the main components. Germanium sulfide glass systems comprise Ge-Ga-Sb-S and Ge-Sb-Sn-S systems, whereas gallium sulfide glass systems comprise Ga-Sb-A-S systems (A = Sn, CsX, (X = Cl, Br, I)). Although these glass systems are free from selenium and arsenic which are commonly used in chalcogenide glasses, they have wide glass-forming composition regions. The glasses are thermally stable against crystallization and can be shaped by molding. Germanium-free gallium sulfide-based glasses are also transparent up to a wavelength of ~13 μm, and their optical window almost covers the atmospheric windows. In addition to the glass-forming regions, the fundamental properties of these glasses including the transmission spectra and refractive indices are presented in this review.