This paper has the following structure: Section \ref{sec:preliminaries} reviews preliminaries such as occupation measures and peak estimation. Section \ref{sec:uncertainty} presents uncertainty models, and a unified uncertain peak estimation model is presented in Section \ref{sec:unified}. Section \ref{sec:discrete} extends uncertain peak estimation to discrete systems. 
The specific case of uncertain peak estimation applied to linear systems analysis are detailed in sections \ref{sec:linear} and \ref{sec:linear_app}
Safety analysis is treated using uncertain peak estimation in section \ref{sec:safety}. 
Other extensions of these techniques are mentioned in \ref{sec:extensions}. 
The paper is concluded in section \ref{sec:conclusion}.