This book provides a thorough survey of the model-based literature on optimal monetary in a stochastic setting. The survey begins with the literature of the 1970s which focused on the information problem in policy design and extends to the New Keynesian approach of the 1990s which centered on evaluating alternative targeting strategies. New to the second edition is consideration of research since the world financial crisis on the role of financial markets and institutions in the conduct of monetary policy. Casting a wide net in this, their second edition, Froyen and Guender provide coverage of the model-based literature on optimal monetary policy in the presence of uncertainty, with both open- and closed-economy frameworks considered. The authors have grounded New Keynesian research of the 1990s and 2000s in the literature of the 1970s, which viewed optimal policy as primarily a question of the optimal use of information, and studies in the 1980s that gave primacy to time inconsistency problems. The Global Financial Crisis of 2007-09 led to the recognition that financial markets and institutions required greater attention in policy modelling. Herein, the authors provide a thorough survey of the post-crisis literature that resulted from this recognition. Researchers in academia and at central banks, students and policy makers will value the wide scope of coverage provided in this examination, leading them to a better understanding of issues such as discretion versus commitment, target versus instrument rules, policy in closed versus open economies and the proper mandate for central banks, including the relationship between interest rate policy and macro-prudential instruments.