As flow instability is a source of turbulence, the topic has been studied by many researchers in fluid dynamics and more broadly in physical sciences to better understand turbulence in geophysical and astrophysical flows. In these large-scale flow systems, stratification and rotation play important roles. Motivated from these, my research has focused on instabilities of shear flows in stratified and rotating fluids. In the seminar, I will give a talk about two topics. The first one will be about Taylor-Couette flow in stably stratified fluids and its two types of instabilities: centrifugal and strato-rotational instabilities. The topic is found to have relevance with equatorial flows in the Earth's ocean and atmosphere. Theoretical and experimental results will be presented to explain the physical mechanism of the two instabilities and demonstrate their nonlinear development leading to turbulence. The second topic of the seminar will be about horizontal and vertical shear flows in stellar radiation zones where stably stratified. More specifically, I will discuss the effects of (i) fast thermal diffusion in the radiation zones and (ii) rotation with the full Coriolis acceleration. I will also discuss how research outcomes on the instability can be used for turbulence modelling in stellar evolution simulations.