The search for a better understanding of nature is an everlasting quest for physicists. While quantum theory predicts most experimental results to date, its interpretation remains highly debated. In the past century, this has kept scientists busy, leading to two seminal theorems that are indispensable to the modern quantum information theoretician: the Bell and Kochen-Specker theorems. On the one hand, the Bell theorem proves that any theory that seeks to explain experimental results must be non-local. On the other hand, the Kochen-Specker theorem examines another feature, akin to non-locality, called non-contextuality. Non-contextuality seems a promising feature at the core of many quantum advantages, such as quantum-computation speedups and oblivious communication. However, providing convincing experimental verification of contextuality is challenging, as tests are prone to imperfections that weaken the logical argument, known as loopholes. Examples of loopholes include the finite-precision loophole, the fact that any realistic measurement is inherently noisy, and the compatibility loophole, in which two consecutive measurements might not be exactly jointly-measurable. Furthermore, contextuality can appear in various settings, including sequential scenarios in which measurements are done one after another on the same system. In that case, the existing notion of non-contextuality becomes obsolete as the assumptions must be accommodated to the sequential setting. Thus, to better appreciate contextuality, we propose two frameworks. First, we focus on the relaxation of outcome determinism and parameter independence, the core assumptions of Kochen-Specker contextuality. We build a framework to handle deviations from these assumptions, enabling us to derive a new notion of non-contextuality that accounts for imperfections. This modified notion of non-contextuality is expressed by a new bound on the contextual fraction—a measure of contextuality—which we prove to be continuous. We also introduce a new measure of signalling called the signalling fraction. This work relates to prior experimental work and demonstrates how the framework accounts for noise in real experimental data. The second framework we present concerns sequential scenarios, in which devices are placed one after another. The specificity of these scenarios, compared to standard measurement scenarios, is that the state can be updated between devices. For that reason, we formalize sequential scenarios, and we define a new notion of contextuality tailored to them. Then we relate non-contextuality to physical assumptions, as the Kochen-Specker theorem, but adapted for sequential scenarios. We also propose a map between sequential and measurement scenarios, under some conditions, which preserves non-contextuality. Altogether, this forms a complete framework, leaving a fertile ground for future research in contextuality within sequential scenarios. In essence, contextuality is a feature of quantum theory, but we might not be able to make sense of contextuality if quantum theory does not accurately represent reality. Within this line of research, the Pusey-Barrett-Rudolph (PBR) theorem proved that, under a reasonable set of assumptions, every pure state of quantum theory is a distinct element of reality. In this thesis, we conduct a preliminary investigation of the PBR theorem and provide a structure for it, generalizing it to other setups. This work also focuses on one central element of this theorem, the notion of overlap, from which we extract new definitions and understanding. This investigation paves the way to new research directions from the PBR theorem. Finally, we complement this thesis with an open-source Python package, available on GitHub and PyPi. The goal of this package is to provide an accessible tool for any researcher in the field of contextuality. We therefore showcase its usage and its usefulness through examples and documentation.