This chapter deals with the class of angelic spaces, introduced by Fremlin, for which several variants of compactness coincide. A remarkable paper of Orihuela introduces a large class of topological spaces X (under the name web-compact) for which the space \(C_p(X)\) is angelic. Orihuela’s theorem covers many already known partial results providing Eberlein–Šmulian-type results. Following Orihuela, we show that \(C_p(X)\) is angelic if X is web-compact. This yields, in particular, Talagrand’s result stating that for a compact space X, the space \(C_p(X)\) is K-analytic if and only if \(C(X)\) is weakly K-analytic. We present some quantitative versions of Grothendieck’s characterization of the weak compactness for spaces \(C(X)\) (for compact Hausdorff spaces X) and quantitative versions of the classical Eberlein–Grothendieck and Krein–Šmulian theorems.