In this article the authors provide a critical analysis of various methodologies involved in "passive replication" of hedge fund returns, a subject that has received renewed interest following recent initiatives by major investment banks. The authors examine from both theoretical and empirical perspectives the benefits and limits of the two different and somewhat competing approaches to hedge fund replication, respectively known as "factor-based replication," and "payoff distribution replication." The analysis suggests that only through the introduction of novel econometric techniques allowing for a parsimonious statistical estimation of the dynamic and/or non-linear functions relating underlying factors to hedge fund returns can hedge fund replication be transformed from an attractive concept into a workable investment solution. The authors conclude that hedge fund replication is still very much a work in progress.