This paper explores the properties of charged black holes in anti-de Sitter (AdS) space-time, focusing on their thermodynamic phase structures in various dimensions. The black holes are solutions to consistent Einstein-Maxwell truncations of gauged supergravities, which arise from including rotation in the transverse space. The authors uncover rich thermodynamic phase structures, including critical phenomena similar to those observed in the van der Waals-Maxwell liquid-gas system. These phases are controlled by universal "cusp" and "swallowtail" shapes from catastrophe theory. The thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can be found on the world volumes of coincident rotating branes. The study begins with an ansatz for obtaining the Einstein-Maxwell truncation of gauged AdS supergravity, which is then used to derive the solutions and compute their actions. The thermodynamic properties of these solutions are analyzed, revealing interesting phase structures at intermediate temperatures. At high temperatures, the physics is dominated by highly non-extreme black holes, leading to "unconfined" behavior characteristic of the associated field theories. At intermediate temperatures, the presence of charge allows for new branches of black hole solutions, modifying the phase structure in the low charge regime. The authors also discuss the dual field theories, which are expected to be related to conformal field theories on the world volumes of rotating branes. They explore the phase structure in both fixed potential and fixed charge thermodynamic ensembles, finding critical points and phase transitions. The phase diagrams are compared to those of the van der Waals system, highlighting the universal nature of the critical phenomena. The paper concludes with a detailed analysis of the specific heat and the approach to the critical point, showing a singularity in the specific heat near the critical temperature.This paper explores the properties of charged black holes in anti-de Sitter (AdS) space-time, focusing on their thermodynamic phase structures in various dimensions. The black holes are solutions to consistent Einstein-Maxwell truncations of gauged supergravities, which arise from including rotation in the transverse space. The authors uncover rich thermodynamic phase structures, including critical phenomena similar to those observed in the van der Waals-Maxwell liquid-gas system. These phases are controlled by universal "cusp" and "swallowtail" shapes from catastrophe theory. The thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can be found on the world volumes of coincident rotating branes. The study begins with an ansatz for obtaining the Einstein-Maxwell truncation of gauged AdS supergravity, which is then used to derive the solutions and compute their actions. The thermodynamic properties of these solutions are analyzed, revealing interesting phase structures at intermediate temperatures. At high temperatures, the physics is dominated by highly non-extreme black holes, leading to "unconfined" behavior characteristic of the associated field theories. At intermediate temperatures, the presence of charge allows for new branches of black hole solutions, modifying the phase structure in the low charge regime. The authors also discuss the dual field theories, which are expected to be related to conformal field theories on the world volumes of rotating branes. They explore the phase structure in both fixed potential and fixed charge thermodynamic ensembles, finding critical points and phase transitions. The phase diagrams are compared to those of the van der Waals system, highlighting the universal nature of the critical phenomena. The paper concludes with a detailed analysis of the specific heat and the approach to the critical point, showing a singularity in the specific heat near the critical temperature.