A univariate sequence is called holonomic, if it satisfies a linear difference equation with polyonomial coefficients. Likewise, a univariate holonomic function satisfies a linear differential equation with polynomial coefficients. In the multivariate (mixed) case, holonomic objects are also characterized through systems of linear difference-differential equations. These equations give a way to finitely represent holonomic objects on the computer. It is well known that based on this representation identities on holonomic expressions can be discovered and proven automatically. Recently with Antonio Jimenez Pastor and Philipp Nuspl, we have studied certain extensions of, e.g., the class of holonomic functions to objects that satisfy linear differential equations with holonomic function coeffiicients and of computational properties that carry over. In this talk, I want to give an overview on the use of the classical algorithms as well as these recent extensions.