Astrophotonics is the application of photonic technologies to channel, manipulate, and disperse light from one or more telescopes to achieve scientific objectives in astronomy in an efficient and cost-effective way. Utilizing photonic advantage for astronomical spectroscopy is a promising approach to miniaturizing the next generation of spectrometers for large telescopes. It can be primarily attained by leveraging the two-dimensional nature of photonic structures on a chip or a set of fibers, thus reducing the size of spectroscopic instrumentation to a few centimeters and the weight to a few hundred grams. A wide variety of astrophotonic spectrometers is currently being developed, including arrayed waveguide gratings (AWGs), photonic echelle gratings (PEGs), and Fourier-transform spectrometer (FTS). These astrophotonic devices are flexible, cheaper to mass produce, easier to control, and much less susceptible to vibrations and flexure than conventional astronomical spectrographs. The applications of these spectrographs range from astronomy to biomedical analysis. This paper provides a brief review of this new class of astronomical spectrographs.