The question of the mechanism giving rise to unconventional superconductivity has been the focus for countless experimental and theoretical efforts for the past three decades. In this thesis, I report on our efforts to better understand the superconducting gap structure in one particular organic unconventional superconductor, κ-(BEDT-TTF) 2 Cu[N(CN) 2 ]Br, and the insights regarding this question that can be gained from the study of previously performed experiments in these materials. Understanding the gap structure in these unconventional superconducting materials is of significant importance, due to the lack of a 'smoking gun' experiment to differentiate between proposed mechanisms. The only method by which the superconductivity can be probed, therefore, is via the properties of the superconducting order parameter, the superconducting gap. This thesis, like any significant work, is the product of one person but the result of a hugely supportive network of people. In the interest of brevity, I will try to limit my thanks to the most important people, without whom I would never have completed this. My primary supervisor, Ben Powell, has given me a tremendous amount of support, direction and advice, for which I am deeply grateful. Ben has consistently motivated and believed in me, even (especially) when I have found myself frustrated with a lack of progress and full of doubt, and I couldn't have asked for a better supervisor. I owe a special thanks to my close friends, office mates and proofreaders, Marco Ho and Amie Khosla, who have helped contribute to my procrastination and excessive caffeination, patiently withstood my complaints any time something went wrong over the past four years, and somehow still offered to proofread this thesis. Thanks as well to my family. You have been unwaveringly supportive of me during my PhD candidature, understanding of how much of my time and concentration has been taken up with this, and infinitely patient with my fumbling attempts at explaining what I've been doing. Most of all, thank you to my partner Sarah Warren. You have been there for me through every day of stress, insecurity, frustration and exhaustion. This process has been at least as stressful for you as for me and you haven't complained about it once. Without your love and support, I couldn't have done any of this. I owe you more gratitude than I can ever hope to show, but I'll keep trying.