This chapter provides an overview of the theory and methods of Punctuated Equilibrium Theory (PET) while drawing examples from European policy-making. It focuses on how organizational and institutional features lead to punctuations in policy-making. The chapter highlights how focusing events, policy ideas, and institutional venues interact and produce periods of stability interspersed with sudden policy changes over time. It introduces recent methodological advances and illustrates how PET relates to the comparative study of policy agendas. PET brings together an underlying individual decision-making and a marco-level policy-process model. As a macro-level process model punctuated equilibrium combines two phases: policy incrementalism and large-scale change. PET scholars mostly rely on Kingdon's idea about how exogenous and endogenous shocks open up "windows of opportunity." PET is a complex theoretical construct. The spontaneity of the proposed processes and their interactive nature make it difficult to construct appropriate research designs and evaluates PET.