  We study the origin of homoclinic chaos in the classical 3D model proposed by
O. R\"ossler in 1976. Of our particular interest are the convoluted
bifurcations of the Shilnikov saddle-foci and how their synergy determines the
global unfolding of the model, along with transformations of its chaotic
attractors. We apply two computational methods proposed, 1D return maps and a
symbolic approach specifically tailored to this model, to scrutinize homoclinic
bifurcations, as well as to detect the regions of structurally stable and
chaotic dynamics in the parameter space of the R\"ossler model.
