Recent works show that there may indeed exist a
non-perturbative continuum definition of quantum field theory (QFT),
at least in some interesting
regimes. I will describe some new ideas from mathematics and physics,
in particular, the  resurgence theory, the trans-series framework from
mathematics and
the idea of adiabatic continuity from physics to provide  new insigths
into the structure of general QFTs.  The new techniques allow us to
determine new saddle points
which play important dynamical roles, e.g.  in confinement,
theta-dependence in semi-classically calculable domains. It also
provides new insights into the nature of IR-renormalon problem. In a
wide class of quantum mechanical systems, these techniques show that
all non-perturbative data is secretly encoded in perturbation theory.