abstract: We prove sharp results about the behaviour of the boundary extensions of forward compositions of inner functions, in relation to shrinking targets and recurrence, inspired by fundamental results about iteration of inner functions, and give examples to illustrate behaviours that cannot occur in the simpler case of iteration (This is joint work with Anna Miriam Benini, Vasso Evdoridou, NĂºria Fagella and Gwyneth Stallard)