  We investigate how loop-level propagators arise from tree level via a
forward-limit procedure in two modern approaches to scattering amplitudes,
namely the BCFW recursion relations and the scattering equations formalism. In
the first part of the paper, we revisit the BCFW construction of one-loop
integrands in momentum space, using a convenient parametrisation of the
D-dimensional loop momentum. We work out explicit examples with and without
supersymmetry, and discuss the non-planar case in both gauge theory and
gravity. In the second part of the paper, we study an alternative approach to
one-loop integrands, where these are written as worldsheet formulas based on
new one-loop scattering equations. These equations, which are inspired by BCFW,
lead to standard Feynman-type propagators, instead of the `linear'-type
loop-level propagators that first arose from the formalism of ambitwistor
strings. We exploit the analogies between the two approaches, and present a
proof of an all-multiplicity worldsheet formula using the BCFW recursion.
