Divisibility of quantum channels and entanglement

I will give a brief summary of the pertinent literature of the latest developments in the divisibility theory of quantum channels. I will focus on the case of qubit channels and I will give the necessary tools to characterize the type of divisibility related with one-parameter semigroups. Later on, and toghether with other types of divisibility, I will present the calculations for the characterizations of almost the whole space of qubit channels. Finally I will comment on the relation of divisibile but not infinitesimal divisible qubit channles with entanglement-breaking.