  This paper is to introduce a new software called CBwaves which provides a
fast and accurate computational tool to determine the gravitational waveforms
yielded by generic spinning binaries of neutron stars and/or black holes on
eccentric orbits. This is done within the post-Newtonian (PN) framework by
integrating the equations of motion and the spin precession equations while the
radiation field is determined by a simultaneous evaluation of the analytic
waveforms. In applying CBwaves various physically interesting scenarios have
been investigated. In particular, we have studied the appropriateness of the
adiabatic approximation, and justified that the energy balance relation is
indeed insensitive to the specific form of the applied radiation reaction term.
By studying eccentric binary systems it is demonstrated that circular template
banks are very ineffective in identifying binaries even if they possess tiny
residual orbital eccentricity. In addition, by investigating the validity of
the energy balance relation we show that, on contrary to the general
expectations, the post-Newtonian approximation should not be applied once the
post-Newtonian parameter gets beyond the critical value $\sim 0.08-0.1$.
Finally, by studying the early phase of the gravitational waves emitted by
strongly eccentric binary systems---which could be formed e.g. in various
many-body interactions in the galactic halo---we have found that they possess
very specific characteristics which may be used to identify these type of
binary systems.
