Fluid mechanics is the study of the behavior of fluids and deformation of the fluid under the influence of shearing forces. One of the most widely used and studied system of equations in fluid mechanics are the Navier-Stokes equations. We study two closely related systems, the magnetohydrodynamics (MHD) equations and the Boussinesq equations. For the MHD equations, we discuss the stabilization effect of a background magnetic field on electrically conducting fluids as well as the construction of a conditional finite time blowup for a 1D transformation of the 2D ideal MHD equations. Additionally, we present the existence and uniqueness of weak solutions to the d-dimensional Boussinesq equations with fractional dissipation and no thermal diffusion.