The study of thermal convection in the presence of rotation, a magnetic field, or both has been the topic of profound interest among researchers for the last several decades. Prototypical models of such systems, based on the Rayleigh-B´enard Convection (RBC), have long been studied to understand various nonlinear phenomena of geophysical and astrophysical systems. The model for RBC, developed by Lord Rayleigh, consists of an infinitely extended thin fluid layer confined between two parallel horizontal plates, with uniform heating of the lower plate from below. Convection manifests as a primary instability when the heating crosses a critical threshold. Interestingly, RBC possesses a rich bifurcation structure near the onset of the primary instability. External forces, such as the rotation, magnetic fields, and the physical properties of the fluid and the confinement, have nontrivial effects on such bifurcation structures. This Seminar will discuss the numerical and analytical investigations on the influence of rotation and/or a magnetic field on various convective instabilities and associated transitions near the onset of a plane layer Rayleigh-B´enard Convection. In this regard, Dr. Mandal will first discuss the effects of rotation in RBC with no-slip boundary conditions. Then, she will discuss the influence of a magnetic field on the dynamics of flow reversals close to the onset of RBC of electrically conducting low Prandtl number fluids. She will conclude by discussing the effects of a magnetic field on the K¨uppers-Lortz instability, which appears in RBC due to rotation.