The aim of this thesis is to investigate the role of both conventional and contemporary mapping techniques and novel ablative modalities to map and to treat these difficult arrhythmias. We investigated the use of a range of mapping systems in examining the substrates for these arrhythmias including body surface 12-lead ECG mapping in patients with a Fontan circulation, contact Halo tricuspid annular activation assessment for right free wall accessory pathways, non-contact mapping in atrial fibrillation, and cryomapping in peri-nodal arrhythmias.  We hypothesised that insights into the arrhythmia substrates will facilitate the design of preventative strategies for Fontan associated arrhythmias as well as enhancing the safety and effectiveness of ablative therapy in the other atrial arrhythmias. Atrial fibrillation is the commonest sustained arrhythmia in humans and is widely acknowledged as the area in electrophysiology in which significant advancements are awaited to improve the efficacy and safety of ablative procedures.  Therefore, the last two chapters were dedicated to investigation of the role of alternative sources of ablative energies and catheter designs in the treatment of atrial fibrillation.  We tested the hypotheses that cryoablation and the focused ultrasound balloon catheter may have distinct advantages over conventional radiofrequency catheters in performing electrical isolation of pulmonary veins for the treatment of patients with atrial fibrillation. In conclusion I synthesize our experience with these cutting edge techniques and place our contribution in the context of the prevailing knowledge of these difficult to treat arrhythmias, undoubtedly the new frontier in cardiac electrophysiology.