We mention some results and examples on rings with finite Gelfand - Kirillov dimension, some open questions and results about extended centers of algebras with quadratic growth with applications. In the case when A is a finitely generated commutative algebra Gelfand-Kirillov dimension is equal to Krull dimension. For this reason Gelfand-Kirillov dimension is a useful tool for obtaining noncommutative analogues of results from classical algebraic geometry. Part of this talk is a joined work with Jason Bell and Tom Lenagan