In contrast to Approximate Factor Models (AFM), our proposed Quantile Factor Models (QFM) allow for unobserved common factors shifting some parts of the distribution other than the means of observed variables in large panel datasets. When such extra factors exist, the standard estimation tools for AFM fail to extract them and their quantile factor loadings (QFL). Two alternative approaches are developed to estimate consistently the whole factor structure of QFM: (i) a two-step estimation procedure which is only valid when the same factors shift the means and the quantiles; and (ii) an iterative procedure which is able to extract (potentially) quantile-dependent factors and their QFL at a given quantile even when both sets of factors differ. Simulation results confirm that our QFM estimation approaches perform reasonably well in finite samples, while four empirical applications provide evidence that extra factors shifting quantiles could be relevant in practice.