The International Conference on Complex Analysis, Potential Theory and Applications was organised by the UCD School of Mathematics and Statistics between 11-15 June 2018. Nearly 80 participants from 22 countries took part in this event which brought together world wide experts in the area of Mathematical Analysis and applications to present their results and address major problems. The event also marked the 60th birthday of Professor Stephne J. Gardiner and was financially supported by Science Foundation Ireland, Irish Mathematical Society, UCD Seed Funding and UCD School of Mathematics and Statistics.