Vertical malocclusions include:
VERTICAL PLANE MALOCCLUSIONS
They can be of two types depending on the vertical overlap of the teeth between the two jaws.
Deep Bite
Here, the vertical overlap between the maxillary and mandibular teeth is in excess of the normal. 
Open Bite
Here, there is no overlap or a gap exists between the maxillary and mandibular teeth when the patient bites in centric occlusion. An open bite can exist in the anterior or the posterior region.
Deep overbite anomalies are categorized into dentally supported deep overbites and gingivally supported deep overbites. Open bite anomalies are divided into anterior, lateral and complex open bites, depending on the localization of the malocclusion.
Ref: Textbook of orthodontics Gurkeerat Singh 2nd ed page no 607, Orthodontic diagnosis- rakosi and graber, page 45
Lateral deep bite
Complex deep bite
Gingivally supported deep bite
Gingivally supported open bite