  The beam longitudinal dynamics code BLonD has been developed at CERN since
2014 and has become a central tool for longitudinal beam dynamics simulations.
In this paper, we present this modular simulation suite and the various physics
models that can be included and combined by the user. We detail the reference
frame, the equations of motion, the BLonD-specific options for radio-frequency
parameters such as phase noise, fixed-field acceleration, and feedback models
for the CERN accelerators, as well as the modeling of collective effects and
synchrotron radiation. We also present various methods of generating
multi-bunch distributions matched to a given impedance model. BLonD is
furthermore a well-tested and optimized simulation suite, which is demonstrated
through examples, too.
