  This review concentrates on the results obtained, over the last ten years, on
the astrophysics of high-energy cosmic ray electrons and positrons. The
anomalies, observed in the data of recent experiments (possible bump in the
electron spectrum and the PAMELA anomaly in the positron fraction) are
discussed through the systematic use of simple analytical solutions of the
transport equations for cosmic ray electrons. Three main ways of explaining the
origin of the anomalies are considered: the conservative way supposing the
positrons to be pure secondary particles; the nearby sources like pulsars
origin; and the dark matter origin. This review discusses, also, the inability
to select the pulsars model or the dark matter model to explain the electron
anomalies on the basis of the electron spectra with the usual large energy
binning ($\gtrsim15%$). It is argued that the signature of nearby pulsars
origin of the anomalies against the dark matter origin could be the fine
structure of the cosmic ray electron spectrum predicted in the Malyshev et al.
paper (2009) and which was observed in the data from the high-resolution ATIC
experiment (2009-2011). To date, the high-resolution ATIC data was the only
experimental result of this type published in the literature. Therefore, they
should be tested by other experiments as soon as possible. Generally, there is,
also, rather controversial situations between the data of the majority of
recent experiments and, consequently, there is a noted urgent need for new
high-precision and high-statistical experiments.
