Motives represent fundamental building blocks for number theory

and geometry. They were postulated by Grothendieck almost sixty years ago,

but there is still no general proof of their existence. Automorphic representations

are spectral objects, with the analytic power one hopes to bring to bear on

motives. They were introduced in the form we now know them by Langlands,

also almost sixty years ago. In this talk, we shall discuss work in progress to

understand some remarkable new relationships that seem to be at the heart

these objects.