  Subtraction schemes provide a systematic way to compute fully-differential
cross sections beyond the leading order in the strong coupling constant. These
methods make singular real-emission corrections integrable in phase space by
the addition of suitable counterterms. Such counterterms may be defined using
momentum mappings, which are parametrisations of the phase space that factorise
the variables that describe the particles becoming unresolved in some infrared
or collinear limit from the variables that describe an on-shell phase space for
the resolved particles. In this work, we review existing momentum mappings in a
unified framework and introduce new ones for final-collinear and soft
counterterms. The new mappings work in the presence of massive particles and
with an arbitrary number of soft particles or of clusters of collinear
particles, making them fit for subtraction methods at any order in perturbation
theory. The new mapping for final-collinear counterterms is also used to
elucidate relations among existing final-collinear mappings.
