The rotor-router model is a deterministic process, in which we place an arrow at every vertex of the underlying graph G, which points to one of its neighbours. A particle then moves on our graph, by first turning the rotor at its current location based on a deterministc ruleset, and then moving towards the new direction of the rotor. A natural generalization of this model is then given, by allowing the turn of the rotor to be itself a random outcome, depending only on the current direction of the rotor. This leads us to defining locally Markov walks, which are stochastic processes, whose next step only depends on the last action the particle performed at its current location. In my talk we will thoroughly define the rotor-router model and discuss one of the main conjectures concerning the behaviour of the walkers, which is whether the rotor-router model with initial directions of the rotors chosen uniformly at random is recurrent on the two-dimensional integer grid. We will also introduce locally Markov walks, and discuss some results of locally Markov walks on finite graphs, as well as several open problems to consider for future research.