  Until fairly recently, it was widely accepted that local cosmic ray spectra
were largely featureless power laws, containing limited information on their
acceleration and transport. This viewpoint is currently being revised in the
light of evidence for a variety of spectral breaks in the fluxes of cosmic ray
nuclei. Here, we focus on cosmic ray electrons and positrons which at the
highest energies must be of local origin due to strong radiative losses. We
consider a pure diffusion model for their Galactic transport and determine its
free parameters by fitting data in a wide energy range: measurements of the
interstellar spectrum by Voyager at MeV energies, radio synchrotron data
(sensitive to GeV electrons and positrons) and local observations by AMS up to
~ 1 TeV. For the first time, we also model the time-dependent fluxes of cosmic
ray electrons and positrons at GeV energies recently presented by AMS, treating
solar modulation in a simple extension of the widely used force-field
approximation. We are able to reproduce all the available measurements to date.
Our model of the interstellar spectrum of cosmic ray electrons and positrons
requires the presence of a number of spectral breaks, both in the source
spectra and the diffusion coefficients. While we remain agnostic as to the
origin of these spectral breaks, their presence will inform future models of
the microphysics of cosmic ray acceleration and transport.
