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.
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