NODYCON 2021 will be hosted as a virtual online conference via ZOOM to overcome the uncertainties of the COVID-19 crisis. The online conference is creatively designed to help corroborate and cement the sense of cohesiveness and liveliness of the NODYCON community. The in-person NODYCON conference is postponed to June 2022. NODYCON 2021 features a rich program with 450+ talks, 18 keynotes and mini-keynotes, two workshops. The talks cover recent advances in the rich spectrum of topics covered by NONLINEAR DYNAMICS, including new frontiers and challenges such as "Complex dynamics of COVID-19: modeling prediction and control". The full-length indexed papers will be published by Springer Nature as "Advances in Nonlinear Dynamics: Proceedings of the Second International Nonlinear Dynamics Conference (NODYCON 2021), Volume 1, 2, 3. A live lecture on Renaissance Arts at the Vatican Museums titled "Through Raphael's eyes. The Renaissance as a vision of beauty and greatness" delivered by Dr. Irene Baldriga, Sapienza University of Rome, is a welcome message for the post-pandemic era. NODYCON 2021 is supported by Sapienza University of Rome, Springer Nature, Polytec, MSC Software Corporation, AIMETA, NODYS.