Stratified shear flow instabilities occur in a variety of physical contexts such as astrophysics, the Earth's atmosphere and oceanography. The linear instability problem has been addressed by a large body of literature resulting in a large variety of stability/instability domains in the Richardson number - wavenumber space, depending on the velocity and stratification profile chosen. I will review some of the old results of stratified shear flows for both piece-wise linear and smooth density and velocity profiles and present new results on the nature of the stability boundaries. These new results are considering smooth flows in which both Kelvin-Helmholtz (non-propagating) and Holmboe (propagating) unstable modes are present. We show how the stability boundaries can be evaluated without solving for the growth rate over the entire parameter space as was previously done. A connection is made with the predictions of piece wise linear models. Finally, I will show that the results indicate further that there is a new instability domain that has not been previously noted in the literature.