  The worldline formalism shares with string theory the property that it allows
one to write down master integrals that effectively combine the contributions
of many Feynman diagrams. While at the one-loop level these diagrams differ
only by the position of the external legs along a fixed line or loop, at
multiloop they generally involve different topologies. Here we summarize
various efforts that have been made over the years to exploit this property in
a computationally meaningful way. As a first example, we show how to generalize
the Landau-Khalatnikov-Fradkin formula for the non-perturbative gauge
transformation of the fermion propagator in QED to the general $2n$ - point
case by pure manipulations at the path-integral level. At the
parameter-integral level, we show how to integrate out individual photons in
the low-energy expansion, and then sketch a recently introduced general
framework for the analytical evaluation of such worldline integrals involving a
reduction to quantum mechanics on the circle and the relation between inverse
derivatives and Bernoulli polynomials.
