With the continuous development of astronomy theory and space exploration technology, searching for extrasolar planets has become one of the most active research topics in astronomy. In recent decades, countries around the world have invested a lot of ground and space projects in this search field and obtained abundant results. Firstly, this paper summarizes the mainstream exoplanet detection methods such as radial velocity, transit and direct imaging method with the outline of the principles and features. Then, several instruments for obtaining the spectrum of exoplanets are introduced, focusing on the optical system parameters of telescopes and spectrometers. Finally, according to the comprehensive discussion above, the future development trend of exploration missions and instrument design in this field is predicted, and it is recognized that these survey missions for detecting and characterizing exoplanets are of great significance for searching biological signals outside the solar system.