The "Complex analysis: techniques, applications and computations" (CAT) programme of 2019 brought together participants from diverse geographical and scientific communities to develop and apply complex analysis to a host of problems from areas including pure and applied mathematics, physics, engineering, and medicine. The Follow-On workshop is an opportunity to consolidate the achievements of the CAT programme and enhance its impact. Its first main goal will be to assess the progress that has taken place in the key thematic areas of the programme. The second main goal will be to formulate new open problems for the community to address in subsequent years. Finally, the workshop will also provide an opportunity to establish new collaborations. The workshop will mirror the structure of the original thematic programme and will cover the following three main overlapping areas: (1) Techniques of complex analysis, including, but not limited to, connections with classical, harmonic and asymptotic analysis, new transform methods, advances in the Wiener–Hopf and Riemann–Hilbert problems; (2) Applications of complex analysis, highlighting connections with diverse areas of modern physics and applied sciences as well as engineering; and n(3) computational complex analysis, including a range of topics bridging mathematical foundations of various numerical techniques and their software implementations.