  The radiation mechanisms responsible for the multiwavelength emission from
relativistic jet sources are poorly understood. The modelling of the spectral
energy distributions (SEDs) and light curves alone is not adequate to
distinguish between existing models. Polarisation in the $X$-ray and
$\gamma$-ray regime of these sources may provide new and unique information
about the jet physics and radiation mechanisms. Several upcoming projects will
be able to deliver polarimetric measurements of the brightest $X$-ray sources,
including active galactic nuclei (AGN) jets and $\gamma$-ray bursts (GRBs).
This article describes the development of a new Monte-Carlo code -- MAPPIES
(Monte-Carlo Applications for Partially Polarised Inverse External-Compton
Scattering) -- for polarisation-dependent Compton scattering in relativistic
jet sources. Generic results for Compton polarisation in the Thomson and
Klein-Nishina regimes are presented.
