This thesis delves into the realm of condensed matter physics, where the discovery of novel quantum states, from unconventional superconductors to non-trivial metallic behaviours, has led to promising applications and intriguing questions regarding the underlying physics. Understanding these non-trivial phenomena demands a combined theoretical and experimental effort. While the exact mechanisms remain under ongoing investigations, it is widely acknowledged that emergent phenomena often arise in the presence of strongly correlated electrons with reduced dimensions, in many cases in proximity to quantum critical points.

This thesis contributes to the exploration of a relatively unexploited and highly fertile collection of van der Waals magnetic insulators known as transition metal phosphorous trichalcogenides, denoted as TMPX₃ (TM = Mn, Fe, Ni, X = S, Se). These compounds have proven to be ideal examples where structural, magnetic and electronic properties evolve into novel states when their dimensionality is tuned with a clean and controllable parameter, pressure. At ambient pressure, they are two-dimensional van-der-Waals antiferromagnets with strongly correlated physics. Recent experimental findings have unveiled pressure induced dimensionality crossover, crystalline structure change, insulator-to-metal transitions and the emergence of novel magnetic phases and superconductivity.

Solving high-pressure structure models, particularly in terms of interplanar stacking geometry, has posed challenges due to the nature of van der Waals materials, which often exhibit mosaicity in single crystals or strong preferred orientation in powder samples. To elucidate the relationships between structural transitions, magnetism and electronic properties, this thesis employs a random structure search using first-principles calculations at high pressures and Density Functional Theory (DFT) + Hubbard U studies. FePS₃ has been chosen as the stereotype compound within the family and has been investigated thoroughly. The coexistence of the low- and intermediate-pressure phases has been carefully examined and explained with theoretical models. Additionally, novel high-pressure phases with distinctive dimensionality and possible alternative options for interpreting the origins of metallicity have been predicted. The validity of the methodology can be extended to other compounds within the family.

The thesis also presents a comprehensive high-pressure synchrotron X-ray study of FePSe₃ using both single crystal and powder samples at the Diamond Light Source. Although FePSe₃ shares a similar intraplanar configuration with FePS₃, it exhibits differences in interplanar stacking at both ambient and elevated pressures. Pressure-induced superconductivity has only been reported in the FePSe₃ so far, occurring at 2.5 K and 9.0 GPa. Despite challenges in defining the crystalline structure models at high pressure, this work provides definitive crystallographic insights into the phases that emerge under pressure. Additionally, magnetic phases have been explored using powder samples within a specially designed pressure cell, with results obtained at the Institut Laue Langevin.