  We present a short overview of the TeV-Halos objects as a discovery and a
relevant contribution of the High Altitude Water \v{C}erenkov (HAWC)
observatory to TeV astrophysics. We discuss history, discovery, knowledge, and
the next step through a new and more detailed analysis than the original study
in 2017. TeV-Halos will contribute to resolving the problem of the local
positron excess observed on the Earth. To clarify the latter, understanding the
diffusion process is mandatory.
