Given a compact complex algebraic surface $S$, the geometric genus $p_g$ of $S$ is the dimension over $\mathbb C$ of the space of holomorphic (or regular) $2$-forms and the irregularity $q$ of $S$ is the dimension of the space of holomorphic (or regular) $1$-forms. The complex projective plane $\mathbb{P}^2$ satisfies $p_g=q=0$, but there are surfaces satisfying $p_g=q=0$ which are not bimeromorphically equivalent to $\mathbb{P}^2$. Although many examples of such surfaces of general type are known, few general results are known.

In this seminar, after a brief historical introduction, some recent general results related to the bicanonical map of surfaces of general type with $p_g=q=0$ will be presented.