This thesis focuses on the study of binary radio pulsars, their evolution and some specific use of their properties to investigate fundamental physics such as general relativity and other gravitational theories. The work that we present here is organized in three main parts. First, we report on the study of PSR J1744-3922, a binary pulsar presenting a peculiar 'flickering' flux behavior as well as spin and orbital properties that do not correspond to the expectations of standard evolution scenarios. We investigated the nature of this flux behavior. We also studied the pulsar's properties in relationship to the binary radio pulsar population and proposed the existence of an as yet unidentified class of binary pulsars. Second, we conducted an in-depth analysis of the eclipses in the relativistic double pulsar system PSR J0737-3039A/B. During these eclipses, the 'A' pulsar partly disappears for ∼ 30s behind its companion, 'B'. The eclipse light curve displays a complex structure of flux modulation that is synchronized with the rotation of pulsar B. We worked on improving our understanding of the eclipse phenomenology and more particularly the modulation phenomenon. From our modeling of the eclipses, we precisely determined the geometry of pulsar B in space and used this information to study the temporal behavior of the eclipses, which revealed that pulsar B precesses around the angular momentum of the system in a way that is consistent with the prediction of general relativity. Third, we searched for the signature of latitudinal aberration in the pulse profile of pulsar A in PSR J0737-3039A/B. This relativistic effect should cause a periodic variation in the separation between the two pulse components of pulsar A on an orbital time scale. The non-detection of this effect allows us to put an upper limit on its amplitude, which constrains the geometry of pulsar A with respect to our line of sight as well as its emission geometry.