On the number of critical points of solutions of semilinear elliptic equations

In this survey we discuss old and new results on the number of critical points of solutions of the problem\begin{document}$ \begin{equation} \begin{cases} -\Delta u = f(u)&in\ \Omega\\ u = 0&on\ \partial \Omega \end{cases} \;\;\;\;\;\;\;\;(0.1)\end{equation} $\end{document}where \begin{document}$ \Omega\subset \mathbb{R}^N $\end{document} with \begin{document}$ N\ge2 $\end{document} is a smooth bounded domain. Both cases where \begin{document}$ u $\end{document} is a positive or nodal solution will be considered.