We will discuss some classification results for Hermitian non-Kähler gravitational instantons. There are three main results: (1) Non-existence of certain Hermitian non-Kähler ALE gravitational instantons. (2) Complete classification for Hermitian non-Kähler ALF/AF gravitational instantons. (3) Non-existence of Hermitian non-Kähler gravitational instantons under suitable curvature decay condition, when there is more collapsing at infinity (ALG, ALH, etc.). These are achieved by a thorough analysis of the collapsing geometry at infinity and compactifications.