  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. Second, we conducted an in-depth
analysis of the eclipses in the relativistic double pulsar system PSR
J0737-3039A/B. 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 the double pulsar system. 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. (Abridged)
