  We introduce collinear drop jet substructure observables, which are
unaffected by contributions from collinear radiation, and systematically probe
soft radiation within jets. These observables can be designed to be either
sensitive or insensitive to process-dependent soft radiation originating from
outside the jet. Such collinear drop observables can be exploited as variables
to distinguish quark, gluon, and color neutral initiated jets, for testing
predictions for perturbative soft radiation in Monte Carlo simulations, for
assessing models and universality for hadronization corrections, for examining
the efficiency of pileup subtraction methods, and for any other application
that leaves an imprint on soft radiation. We discuss examples of collinear drop
observables that are based both on clustering and on jet shapes. Using the
soft-collinear effective theory we derive factorization expressions for
collinear drop observables from QCD jets, and carry out a resummation of
logarithmically enhanced contributions at next-to-leading-logarithmic order. We
also identify an infinite class of collinear drop observables for which the
leading double logarithms are absent.
