A number of recent papers have argued that US firms exert increasing market power, as measured by their markups of price over marginal cost. I review three of the main approaches to estimating economy-wide markups and show that all are based on the hypothesis of firm cost minimization. Yet different assumptions and methods of implementation lead to quite different conclusions regarding the levels and trends of markups. I survey the literature critically and argue that some of the startling findings of steeply rising markups are difficult to reconcile with other evidence and with aggregate data. Existing methods cannot determine whether markups have been stable or whether they have risen modestly over the past several decades. Even relatively small increases in markups are consistent with significant changes in aggregate outcomes, such as the observed decline in labor’s share of national income.