After a ical introduction to heights, we discuss various generalisations of Lehmer's problem. The framework is that of normalized heights on abelian varieties and tori. We include the study of obstruction indices, relative at the same time to an arbitrary ground field and to an algebraic subgroup. We introduce the notion of a Lehmer group to unify our statements. Usual examples correspond to the trivial group ( ical Lehmer's problem), the torsion group (relative Lehmer's problem) or the whole group of algebraic points (effective Bogomolov's problem) but we show that also all finite rank subgroups are of interest, even in the one-dimensional case. We then discuss the applications of such height lower bounds to the Zilber-Pink conjecture. We show how all the variants quoted can be used to provide a crucial step toward the conjecture : once one knows (by other methods) that the height of the intersection under consideration is bounded, the Lehmer-like bounds allow to get finiteness.