The core of my research are models in the so-called Kardar-Parisi-Zhang universality class. They includes interacting particle systems, stochastic growth models, but also random polymer and random tiling models. At large time, one observes universal behaviors, for instance, for the current of particles or for the interface height function. Interestingly, the limiting distributions are not Gaussian and they occurs also in random matrix theory. The methods used in my research span from probabilistic, algebraic and analytic methods, and numerical methods. In the current recent research, the focus is more on non-exactly solvable models.