Given $B \subset N$, we consider the corresponding set $FB$ of $B$-free integers, i.e. $n \in FB i_ no b \in B$ divides $n$. We $de_{ne} X \eta_}$ the B-free subshift _ as the smallest subshift containing $\eta := 1FB \in {0, 1}Z$. Such systems are interesting both from the dynamical and number theoretical viewpoint and can manifest various types of behavior. I will concentrate on the entropy and its generalization _ topological pressure, with some applications in combinatorics / number theory. Talk will be based on a joint work with Michael Lemanczyk and Michael Rams.