  The near-completion of the program of endoscopy poses the question of what
lies next. This article takes a broad view of ideas beyond the program of
endoscopy, highlighting the connections among them, and emphasizing the
relationship between local and global aspects. Central among those ideas is the
one proposed in a 2000 lecture of R. P. Langlands, aiming to extract from the
stable trace formula of a group G the bulk of those automorphic representations
in the image of the conjectural functorial lift corresponding to a morphism of
L-groups ${^LH} \to {^LG}$. With the extension of the problem of functoriality
to the "relative" setting of spherical varieties and related spaces, some
structure behind such comparisons has started to reveal itself. In a seemingly
unrelated direction, a program initiated by Braverman--Kazhdan, also around
2000, to generalize the Godement--Jacquet proof of the functional equation to
arbitrary L-functions, has received renewed attention in recent years. We
survey ideas and developments in this direction, as well, and discuss the
relationship between the two programs.
