The notion of a girth was first introduced by S. Schleimer in 2003. Later, a substantial amount of work on the girth of finitely generated groups was done by A. Akhmedov, where he introduced the so-called Girth Alternative and proved it for certain classes of groups, e.g. hyperbolic, linear, one-relator, $P{L}_{+}(I)$ etc. Girth Alternative is similar to the well-known Tits Alternative in spirit, therefore it is natural to study it for classes of groups for which Titis Alternative has been investigated. In this talk, we will explore the girth of HNN extensions of finitely generated groups in its broadest sense by considering cases where the underlying subgroups are either full or proper subgroups. We will present a sub-class for which Girth Alternative holds. We will also produce counterexamples to show that beyond our class, the alternative fails in general. Recently, we extended one of the main results proving the Girth Alternative for HNN extensions of word hyperbolic groups (instead of HNN extensions of free groups). The talk will be based on joint work with Azer Akhmedov.