We demonstrate that major asymmetries in erupting filaments and CMEs, namely major twists and non-radial motions are typically related to the larger-scale ambient environment around eruptive events. Our analysis of prominence eruptions observed by the STEREO, SDO and SOHO spacecraft shows that prominence spines retain, during the initial phases, the thin ribbonlike topology they had prior to the eruption. This topology allows bending, rolling, and twisting during the early phase of the eruption, but not before. The combined ascent and initial bending of the filament ribbon is non-radial in the same general direction as for the enveloping CME. However, the non-radial motion of the filament is greater than that of the CME. In considering the global magnetic environment around CMEs, as approximated by the Potential Field Source Surface (PFSS) model, we find that the non-radial propagation of both erupting filaments and associated CMEs is correlated with the presence of nearby coronal holes, which deflect the erupting plasma and embedded fields. In addition, CME and filament motions respectively are guided towards weaker field regions, namely null points existing at different heights in the overlying configuration. Due to the presence of the coronal hole, the large-scale forces acting on the CME may be asymmetric. We find that the CME propagates usually non-radially in the direction of least resistance, which is always away from the coronal hole. We demonstrate these results using both low and high latitude examples.