  Orbital parameters of binary radio pulsars reveal the history of the pulsars'
formation and evolution including dynamic interactions with other objects.
Advanced technology has enabled us to determine these orbital parameters
accurately in most of the cases. Determination of post-Keplerian parameters of
double neutron star binaries (especially of the double pulsar) provide clean
tests of GTR and in the future may lead us to constrain the dense matter EoS.
For binary pulsars with MS or WD companions, knowledge about the values of the
orbital parameters as well as of the spin periods and the masses of the pulsars
and the companions might be useful to understand the evolutionary history of
the systems. As accreting neutron star binaries lead to orbit circularization
due to the tidal coupling during accretion, their descendants i.e. binary MSPs
are expected to be in circular orbits. On the other hand, dense stellar
environments inside globular clusters (GCs) cause different types of
interactions of single stars with pulsar binaries. These interactions can
impart high eccentricities to the pulsar binaries. So it is quite common to get
eccentric millisecond pulsar binaries in GCs and we find that "fly-by" causes
intermediate values of eccentricities while "exchange" or "merger" causes high
values of eccentricities. We also show that "ionization" is not much effective
in the present stage of GCs. Even in the absence of such kinds of stellar
interactions, a millisecond pulsar can have an eccentric orbit as a result of
Kozai resonance if the pulsar binary is a member of a hierarchical triple
system. PSR J1903+0327 is the only one eccentric millisecond pulsar binary in
the galactic disk where stellar interactions are negligible. The possibility of
this system to be a member of a hierarchical triple system or past association
of a GC have been studied and found to be less likely.
