Let $\Cal F$ be a holomorphic foliation (possibly with singularities) on a non-singular manifold $M$, and let $V$ be a complex analytic subset of $M$. Usual residue theorems along $V$ in the theory of complex foliations require that $V$ be tangent to the foliation (that is, a union of leaves and singular points of $V$ and $\Cal F$); this is the case for instance for the blow-up of a non-dicritical isolated singularity. In this paper, residue theorems are introduced along subvarieties that are not necessarily tangent to the foliation, including the blow-up of the dicritical situation.