The present manuscript, submitted as Habilitation Thesis in view of the \emph{Habilitation \`a diriger la recherche}, presents an important part of my recent and current research work on the possibility of Non-Minimal Flavour Violation within supersymmetric theories. The first part of this manuscript contains an introduction to the concept of flavour and its description, first within the Standard Model of particle physics, then in theories beyond the latter. A dedicated discussion of the Minimal Supersymmetric Standard Model (MSSM) allows to introduce the framework of Non-Minimal Flavour Violation. The second part of this manuscript is composed of a selection of published work to which I have significantly contributed mainly between 2013 and 2018. I review in particuler work on experimental signatures of Non-Minimal Flavour Violation in the squark sector of the MSSM. In addition, I discuss the implementation of Non-Minimal Flavour Violation within Grand Unified frameworks including flavour symmetries. In the third and last part of this manuscript, I briefly discuss ongoing and future projects, to be understood as perspectives stemming from the presented published work.