  Secondary positrons are produced by spallation of cosmic rays within the
interstellar gas. Measurements have been typically expressed in terms of the
positron fraction, which exhibits an increase above 10 GeV. Many scenarios have
been proposed to explain this feature, among them some additional primary
positrons originating from dark matter annihilation in the Galaxy. The PAMELA
satellite has provided high quality data that has enabled high accuracy
statistical analyses to be made, showing that the increase in the positron
fraction extends up to about 100 GeV. It is therefore of paramount importance
to constrain theoretically the expected secondary positron flux to interpret
the observations in an accurate way. We find the secondary positron flux to be
reproduced well by the available observations, and to have theoretical
uncertainties that we quantify to be as large as about one order of magnitude.
We also discuss the positron fraction issue and find that our predictions may
be consistent with the data taken before PAMELA. For PAMELA data, we find that
an excess is probably present after considering uncertainties in the positron
flux, although its amplitude depends strongly on the assumptions made in
relation to the electron flux. By fitting the current electron data, we show
that when considering a soft electron spectrum, the amplitude of the excess
might be far lower than usually claimed. We provide fresh insights that may
help to explain the positron data with or without new physical model
ingredients. PAMELA observations and the forthcoming AMS-02 mission will allow
stronger constraints to be aplaced on the cosmic--ray transport parameters, and
are likely to reduce drastically the theoretical uncertainties.
