Over the field of complex numbers, one understands the relation between the étale fundamental group, which is the profinite completion of the topological one, with the local systems, or, equivalently, with regular singular algebraic flat connections. In short, the étale fundamental group controls the local systems. In characteristic $p>0$, we don’t understand yet the corresponding statement fully, except when $X$ is projective. We will discuss natural problems and conjectures.