In this chapter, we want to investigate mean ergodic bi-continuous semigroups by means of Cesáro means. We will also see that those semigroups have applications to Feller semigroups generated by autonomous and non-autonomous second-order differential operators with unbounded coefficients in \(\textrm{C}_{\textrm{b}}(\mathbb {R}^N)\) . The basic idea of mean ergodicity is that the time mean equals the space mean within a dynamical system. This so-called ergodic hypothesis goes back to Boltzmann [44] which has been mathematically accentuated later on by Birkhoff [40] and von Neumann [235]. The most common technique is the linearization of dynamical systems by means of Koopman operators which actually gives the chance to pass from dynamics to linear operators, and back. The fundamental concepts of this operator theoretical approach can, for example, be found in [94]. The interest in such operators has its origins appearing in the context of statistical mechanics and probability theory highly motivate these kind of operators.