The analytic spread of a module M is the minimal number of generators of a submodule that has the same integral closure as M. In this talk, we will present a result that expresses the analytic spread of a decomposable module in terms of the analytic spread of its component ideals. In the second part of the talk, we will show an upper bound for the symbolic analytic spread of ideals of small dimension. The latter notion is the analogue of analytic spread for symbolic powers. These results are joint work with Carles Bivià-Ausina and Hailong Dao, respectively.