<p>The understanding of non-Newtonian two-phase flows is a far from easy issue because two-phase flows dynamically and intricately behave through boundary interfaces with the local variation in rheological properties. A key factor to explore structures and mechanisms of non-Newtonian two-phase flows is to perceive a local profile of non-Newtonian properties corresponding to the shear-rate. In this article, I review current situation and challenges about the study of non-Newtonian two-phase flows through the author' s studies on the dynamic motion of bubbles and drops in non-Newtonian fluids.</p>