Upon approaching the glass transition a liquid gets extremely sluggish without obvious structural changes. Despite decades of work, the physical origin of this glassy slowdown remains controversial. A common explanation relies on the increasing roughness of the underlying free-energy landscape, but the theoretical and experimental underpinnings of this scenario are still lacking. In this talk, I will survey recent advances that let us unambiguously identify and track the growing amorphous order, a manifestation of the rarefaction of metastable states in the rugged landscape. I will further explore the crucial role this order plays in driving the glassy slowdown.