This issue of Astérisque presents some recent work in the fields of (co)homology and finite length representations of Lie groups. In homology theory proofs are given of Shapiro's lemma, of the regularization theorem (i.e. the isomorphism between $H_{*}(G,E)$ and $H_{*}(G,E_{\infty})$ when $E$ is a continuous $G$-module), and of the surjectivity of the map $H_{*}(G_{d},E) \to H_{*}(G,E)$, where $G_{d}$ denotes the abstract group underlying $G$. The problems of computing $Ext^{n}$ between irreducibles and of studying finite length representations are considered for various classes of Lie groups $G$ : real semisimple, nilpotent, and semidirect products $G = B\times A$ with $B$ a vector group, and for suitable irreducible represen-tations of $G$. In the semisimple (resp. nilpotent) case one obtains algebraic descriptions in terms of the Langlands classification (resp. the orbit method). In the case of semidirect products the aim is to obtain a reduction theorem in the spirit of Mackey's theory; under certain hypotheses, this can be carried out completely.