Scientists are increasingly relying on astronomical and remote sensing technologies to gain deeper insights into the Earth and the universe. In these fields, the optical spectrum analyzer (OSA) or spectrometer plays a pivotal role. This Review offers a comprehensive overview of the fundamental principles, key parameters, and applications of various branches of traditional OSAs, including prisms, gratings, interferometers, tunable filters, and reconstructive spectrometers. We specifically focus on their latest major applications in astronomy and remote sensing. Additionally, we present a mathematical model of the generalized reconstructive spectrometer and provide a summary of its principles pertaining to spectral mapping, reconstruction, and imaging. Despite its limited aperture and étendue, the reconstructive spectrometer holds great potential for future use in astronomy and remote sensing due to its compact size and exceptional ultrahigh spectral resolution.