This concisely written paper combines a survey of the standard facts about the structure of locally compact groups and their approximation by Lie groups with an exposition of the resulting structural similarities between locally compact groups of finite dimension and Lie groups. It pinpoints (and sometimes corrects) many facts that have been floating in the folklore of the subject and provides a firm grip on those tools that are most useful in applications. Let \(G\) be a locally compact, connected group of finite dimension. The author introduces the ``rough structure'' of \(G\), i.e., the lattice of its closed, connected subgroups together with the relations ``\(A\) normalizes (or centralizes) \(B\)''. He shows that epimorphisms with compact, totally disconnected kernels induce isomorphisms of the rough structures. (The example \(\mathbb{R}^2/ \mathbb{Z}^2\) shows the necessity of the compactness condition.) In particular, \(G\) can be approximated by a Lie group whose rough structure is isomorphic to that of \(G\). The structure of compact groups as well as product decompositions and automorphisms of locally compact abelian groups are treated. It is shown how the notion of (semi-)simplicity and the theory of Iwasawa and Levi decompositions can be developed in a very direct way for the groups under consideration, without permanent recourse to an approximating projective system of Lie groups. The possibilities for non-Lie groups approximated by simple Lie groups are determined (despite some folklore tradition saying that such groups do not exist). Following \textit{A. M. Gleason} [Am. J. Math. 78, 797-807 (1956; Zbl 0072.380)] and \textit{A. M. Gleason} and \textit{R. S. Palais} [Am. J. Math. 79, 631-648 (1957; Zbl 0084.032)], the refined topology of \(G\) having for a basis the arcwise connected components of the open sets of \(G\) is introduced. The theorem of Gleason and Palais stating that this makes \(G\) a Lie group is neatly proved, and the relationship of the two topological groups is clarified. Finally, it is indicated how information on the rough structure of \(G\) may be obtained by applying results on complex algebraic groups.