At the boundary of (discrete) probability and statistical physics, random walks in dynamic environments represent a way to model a particle advected by a fluid. Though some models are quite simple to define (usually, the environment is an evolving particle system, such as the exclusion process or a "cloud" of random walks), interest for this topic among probabilists has strongly increased in the past decade. These models feature complex technical challenges, as the time-dependency of the environment totally reshuffles the structure of space-time correlations, compared to the more classical setting of walks in static environment. In this talk, we will present this context and highlight how some key features such as recurrence/transience or the fluctuations of the walker are still the subject of many conjectures.