The research area of ​​detecting exoplanets, planets outside our own solar system, is a huge area of ​​interest and funding. The importance of being able to detect these planets is that they can provide us with information and insight into planetary formation, to aid in the search for "Earth-like" planets in the habitable zone, and of course the ever-present question of extraterrestrial life. So to try to gather information about these things, we need to have robust detection techniques for exoplanets. Some of the important methods will be discussed here including radial velocity method, transit method, direct imaging, and gravitational microlensing among others. The radial velocity method, also known as the Doppler spectroscope/exoplanet detection method, is based on the principles that a star that has a planet in its orbit will experience a gravitational force from the planet and will therefore move on its own small orbit in response. This will cause changes in the speed of the star as it moves closer and further away from the observer, i.e. the Earth, and this will be seen as variations in the radial speed of the star in relation to the Earth. The radial velocity of the star can be calculated from the shift of the spectral lines in the star's spectra due to the Doppler effect and from there the variations can be determined and if they apply, the presence of an exoplanet can be confirmed. High precision spectrometers such as HARPS are required to perform observations with a very high signal-to-noise ratio. HARPS is a high-resolution fiber-powered scale spectrograph. To maximize the chances of detecting an exoplanet, certain conditions must be met by potential targets. The targets chosen to be studied by HARPS are selected from COR...... middle of paper ...... Experiment” (OGLE) are two missions that monitor these microlensing events. Planets around low-mass stars are easier to detect with this method because the ratio of the mass of the planet to that of the stars will increase and therefore the gravitational microlensing effect will be greater. The characteristic scale of gravitational microlensing is the radius of Einstein's ring RE. The Einstein ring occurs when the lens and source are aligned and the light from the source is shaped into a ring through the gravitational lens by the gravitational field of the "lens" object. R = Works cited - Baranne, A. et al. 1996, A&AS, 119,373 - Bond, IA et al., 2002, MNRAS 333, 1, 71-83 - Figueira, P. et al., 2013, A&A, 557, A93 - Koch, D. et al. 2010, ApJ, 713, L131-L135- Mandel, K. & Agol, E. 2002, ApJ, 580, L171- Sumi, T. et al. 2011, Nature, 473, 349-352- Udry, S. et al. 2000, A&A, 356, 590