In this thesis I explore the advantages of measuring precise radial velocities in the infra-red domain, and how it can be employed to detect extrasolar planets. After an introduction on the state of the art of extrasolar planet searches, I describe the radial velocity method, the most effective to date in detecting extrasolar planets. I describe its fundaments, as well as its advantages and disadvantages. I move then to the infra-red domain, I describe the peculiarities of infra-red spectrographs, and the characteristics of the one I used during my thesis, CRIRES. I present some interesting cases - and publications - on which infra-red radial velocities were paramount to our understanding of the nature of radial-velocity and I conclude with prospects on future works.