  In the last years there have been several new constructions of surfaces of
general type with $p_g=0$, and important progress on their classification. The
present paper presents the status of the art on surfaces of general type with
$p_g=0$, and gives an updated list of the existing surfaces, in the case where
$K^2= 1,...,7$. It also focuses on certain important aspects of this
classification.
