A chemically active microdrop that is suspended in the bulk of a reagent solution is an example of a non-equilibrium physicochemical system akin to cells and vesicles. Owing to their non-equilibrium nature, active drops may excite the flow in the surrounding fluid even in the absence of preexisting asymmetries, such as gravity or inhomogeneous interfacial properties. In experiments, this spontaneous flow excitation results in active drops self-deforming or self-propelling along a straight, helical, or chaotic trajectory. In this talk, we will discuss two theoretical models that explain self-propulsion regime selection based on droplets' interfacial properties. The first model corresponds to the case of a slow chemical reaction and demonstrates that in active drops of nematic liquid crystal, coupling of the flow field and liquid crystal configuration may result in a novel mode of orientational instability. Numerical solution of the model equations in 3D reveals that this instability leads to helical self-propulsion trajectory. The second model focuses on the case of intense chemical reaction. We consider a drop undergoing micellar dissolution and demonstrate that continuous assembly of swollen micelles may act as a cleaning mechanism for the droplet interface, thus significantly affecting the onset of self-propulsion. Moreover, as the kinetics of micelles production is inherently nonlinear, drop self-propelling behavior depends heavily on the sorption and reaction rates.