Fenestrated/branched endovascular aortic repair emerges as the primary therapeutic modality for intricate aortic pathologies encompassing the paravisceral and thoracoabdominal segments, where bridging stent grafts (BSGs) play a vital role in linking the primary aortic endograft with target vessels. Bridging stent grafts can be categorized mainly into self-expanding stent grafts (SESGs) and balloon-expandable stent grafts (BESGs). Physiological factors significantly influence post-complex endovascular aortic repair BSG behaviour, impacting clinical outcomes of SESGs and BESGs in different but overlapping ways. Crucial prerequisites for BSGs encompass not only flexibility but also resilience against mechanical stress and compliance mismatch, especially when bridging the rigid aortic main body with dynamic target vessels. The significance of considering these physiological factors in clinical decision-making is underscored by recognizing the interplay between SESG and BESG characteristics, vessel physiology and patient haemorheology. Such factors include the anatomy and tortuosity of the vessel, diameter of the vessel and BSG, deployment and durability, extrinsic stenosis and respiratory motion. Haemorheological factors, such as anti-thrombotic therapy and hydration status, need to be considered. This narrative review examines both in vitro and in vivo evidence regarding the impact of physiological factors on the behaviour of BSGs and assesses the consequences for clinical outcomes following complex endovascular aortic repair.