Atomic clocks are today essential for several daily life applications, such as the building of the International Atomic Time (TAI) or Global Navigation Satellite Systems (GNSS). With the new generation of optical clocks, they reach such accuracy and stability that they are now considered in practical applications for the measurement of gravitational potential differences, thanks to the Einstein effect, or gravitational redshift. Several projects explored the possibilities of using clocks in geodesy or geophysical applications and research. This context offers a fantastic opportunity to use atomic clocks to test fundamental physics. In this talk I will present two such studies for testing the gravitational redshift and Lorentz invariance.The first project is the "Galileo gravitational Redshift test with Eccentric sATellites" (GREAT), funded by the European Space Agency (ESA). Here we use the on-board atomic clocks of the Galileo satellites 5 and 6 to look for violations of general relativity theory. These two satellites were launched on August, 30th 2014 and, because of a technical problem, the launcher brought them on an elliptic orbit. An elliptic orbit induces a periodic modulation of the gravitational redshift while the good stability of recent GNSS clocks allows to test this periodic modulation to a very good level of accuracy. The Galileo 5 and 6 satellites, with their large eccentricity and on-board H-maser clocks, are hence perfect candidates to perform this test.In the second study we propose a test of special relativity theory using a network of distant optical lattice clocks located in France, Germany and Great-Britain. By exploiting the difference between the velocities of each clock in the inertial geocentric frame, due to their different positions on the surface of the Earth, we can test the time dilation effect. The connection between these clocks, achieved with phase-compensated optical fibers, allows for an unprecedented level of statistical resolution for the comparison of remote atomic clock, making such a test now competitive with the best Ives-Stillwell tests.