The notion of disjointness was introduced to the topological dynamics by Furstenberg in his seminal paper from 1967. Recall that two TDSs (X,f), (Y,g) are disjoint if their only joining (i.e. invariant subset of X×Y whose projections are X and Y respectively) is X×Y and are weakly disjoint if their Cartesian product f×g is transitive. In this talk we will focus on some aspects of disjointness and weak disjointness related to topological weak mixing.