  Theoretical issues are discussed for the measurement of the top-mass using
jets, including perturbative and non-perturbative effects that relate
experimental observables to the Lagrangian mass, and appropriate choices for
mass schemes. Full account for these issues is given for e+e--> t-tbar using a
factorization theorem for event shapes for massive quarks. Implications for the
Tevatron top-mass measurement are discussed. A mass-scheme, the "MSR-mass", is
introduced which allows for a precise description of observables sensitive to
scales R << m, but at the same time does not introduce perturbative matching
uncertainties in conversion to the MSbar mass.
