We characterize positive links in terms of strong quasipositivity, homogeneity, and thevalue of Rasmussen and Beliakova-Wehrli's
$s$ -invariant. We also study almost positive links, and inparticular, determine the
$s$ -invariants of almost positive links. This result suggests that all almostpositive links might be strongly quasipositive. On the other hand, it implies that almost positivelinks are never homogeneous links.