The spectrum of positrons in cosmic rays is currently measured with unprecedented precision by AMS-02 up to TeV energies, and represents an unique probe for the local properties of our Galaxy. Currently, its interpretation is still debated, especially for the excess above 10 GeV which suggests the presence of a local, primary source.
Recently, the observation of extended gamma-ray halos around Galactic pulsars has opened a new window to constrain the acceleration and propagation of positrons in our Galaxy.
These gamma-ray structures, observed from GeV to multi TeV energies, are the result of inverse Compton scattering of electrons and positrons  accelerated at the pulsar’s wind termination shock and propagating in the turbulent interstellar medium.
However, many aspects remain unclear: How are these halos formed? Are they a general property of Galactic pulsars? What are the consequences for cosmic-ray acceleration and propagation in our Galaxy?
I will introduce our current understanding of the positron spectrum in cosmic rays, focusing on pulsars.  I will discuss the most recent theoretical and observational developments on pulsar halos at different wavelengths, and conclude by outlining some perspectives to shed light on the open questions in the near future.