The conference « Scale Invariance and Randomness », which will take place next to Lille (north of France) from 7 June 2022 to 10 June 2022, is a part of a thematic semester on Probability and Statistics organized by the Laboratory Paul Painlevé (Université de Lille). The event is associated with the French GDR 3475 « Analyse Multifractale et Autosimilarité ». The purpose is to bring together researchers from all over the world in order to explore various aspects of self-similar stochastic processes and their applications. The topics of the conference include, among others, stochastic analysis, fractal geometry, multifractal analysis, stochastic partial differential equations, statistical inference for stochastic processes, limit theorems, long memory, Stein's method, fractional and multifractional processes, random series, and wavelet methods.