It is well known that, within the usual instrumental variable model where a randomized treatment is affected by non compliance, the instrumental variable estimand may be interpreted as an average causal effect on the treated, on the compliers, or on the overall population, depending on certain additional assumptions. We propose a new derivation which: (i) extends most known results from binary to partial compliance, (ii) provides new insights on the effect of treatment on the treated and suggests a new extension of the IV estimand, (iii) clarifies the relationship with the structural marginal models and (iv) provides a translation of the principal strata formulation into a non parametric structural model and clarifies the relation between the effect of treatment on compliers relative to that on the treated.