In recent years several authors have developed algorithms in the parameterized Galois theory for linear differential equations with differential parameters and the differential Galois theory for linear difference equations. The Galois groups that arise in these theories are linear differential algebraic groups, and their structure encodes the differential-algebraic properties of the solutions of the equations; in particular whether these solutions are hypertranscendental. In this overview lecture we will survey recent algorithmic developments in these theories, and the techniques that underly them.