The Goldie dimension of a module M is defined as the supremum of all cardinalities λ such that M contains the direct sum of λ nonzero submodules. This definition can be easily extended to modular lattices with 0 and it extends the notion of the linear dimension of linear spaces to modules or, further, to modular lattices. It is natural to ask how far the fundamental properties of the linear dimension can be extended to the Goldie dimension. Problems of that sort were studied in many papers. The aim of the talk is to present some old and new results concerning that topic.