A large fraction of the eligible unemployed workers does not claim for unemployment insurance (UI) and, among claimants, many do not register immediately upon layoff. This paper argues that, to understand this intriguing phenomenon, one needs to model jointly job search and take-up efforts and to allow for heterogeneity in both dimensions. Estimating such a model using French administrative data, we find substantial heterogeneity in both search and claiming frictions. If half of the sample faces high claiming frictions, many have good employment prospects and exit unemployment quickly. The burden of the claiming difficulties is concentrated on 10% of the sample that suffers both from claiming and job search difficulties. For that reason, the alleviation of the complexity of the claiming process is likely to have very heterogenous effects but little effect on aggregate unemployment duration. Additionally we show that the link between claiming and job search efforts has important implications when measuring how UI parameters impact unemployment duration.