This article provides an accessible introduction to the phenomenon of monotone likelihood in duration modeling of political events. Monotone likelihood arises when covariate values are monotonic when ordered according to failure time, causing parameter estimates to diverge toward infinity. Within political science duration model applications, this problem leads to misinterpretation, model misspecification and omitted variable biases, among other issues. Using a combination of mathematical exposition, Monte Carlo simulations and empirical applications, this article illustrates the advantages of Firth's penalized maximum-likelihood estimation in resolving the methodological complications underlying monotone likelihood. The results identify the conditions under which monotone likelihood is most acute and provide guidance for political scientists applying duration modeling techniques in their empirical research.