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. 
Section \ref{sec:safety} presents the application of uncertain peak estimation to safety analysis.
% Efficacy is demonstrated in section \ref{sec:examples}, and t
The paper is concluded in Section \ref{sec:conclusion}.