Many patients lack the required alveolar bone height to safely place dental implants for tooth replacement. A number of techniques can be used to vertically augment deficient jaws, but each is associated with limitations and complications that make contemporary bone tissue engineering (TE) methods an attractive alternative. Bone TE is a rapidly evolving field with numerous promising developments; however, the complexity of the structure and healing of natural alveolar bone make it difficult to define an ideal bone substitute, which should combine space maintenance and osteoconduction/induction. Indeed, currently available vertical alveolar bone-replacement approaches are unable to achieve predictable clinical outcomes. This review outlines the need for new approaches to vertical alveolar bone augmentation in which additive manufacturing plays a central role and can be considered as one of the most promising future developments from a clinical perspective.