Congenital heart disease (CHD) affects around 1.35 million neonates worldwide per annum, and surgical repair is necessary in approximately 25% of cases. Xenografts, usually of bovine or porcine origin, are often used for the surgical reconstruction. These xenografts elicit an immune response due to significant immunological incompatibilities between host and donor. Current techniques to dampen the initial hyperacute rejection response involve aldehyde fixation to crosslink xenoantigens, such as galactose-α1,3-galactose and N-glycolylneuraminic acid. While this temporarily masks the epitopes, aldehyde fixation is a suboptimal solution, degrading over time, resulting in cytotoxicity and rejection. The immune response to foreign tissue eventually leads to chronic inflammation and subsequent graft failure, necessitating reintervention to replace the defective bioprosthetic. Decellularisation to remove immunoincompatible material has been suggested as an alternative to fixation and may prove a superior solution. However, incomplete decellularisation poses a significant challenge, causing a substantial immune rejection response and subsequent graft rejection. This review discusses commercially available grafts used in surgical paediatric CHD intervention, looking specifically at bovine jugular vein conduits as a substitute to cryopreserved homografts, as well as decellularised alternatives to the aldehyde-fixed graft. Mechanisms of biological prosthesis rejection are explored, including the signalling cascades of the innate and adaptive immune response. Lastly, emerging strategies of intervention are examined, including the use of tissue from genetically modified pigs, enhanced crosslinking and decellularisation techniques, and augmentation of grafts through recellularisation or functionalisation with human surface proteins.