(1) Background: Treating dental luxation injuries is challenging for the clinician. Dental luxations account for 18–33% of injuries to permanent teeth and can be addressed using different therapeutic approaches. The present work was conducted with two aims: (i) to evaluate, through a scoping review, current knowledge of the orthodontic methods (repositioning and stabilization splinting) that can be used at the time of the trauma, and (ii) to investigate the frequency and type of pulp consequences arising after these traumatic injuries. (2) Methods: The literature search was conducted in the period June 2020–December 2020 using the PubMed/MEDLINE, SCOPUS and Web of Science databases. The research questions were formulated according to the PICO (Population, Intervention, Comparison, Outcomes) method and considered the following aspects: type of luxation injury and stage of root development; use of orthodontic repositioning and splinting techniques; frequency and type of pulp consequences; and compliance of treatments with international guidelines. (3) Results: The initial screening of the databases, using the selected search keywords, yielded a total of 587 articles, just 8 fully met the inclusion criteria. Closer analysis of these 8 publications revealed that they would not produce clear meta-analytical data. This made it necessary to limit the data collected to the following six items: number and type of injuries, initial therapeutic intervention, duration of follow-up, number, and type of different pulp consequences. (4) Conclusions: While orthodontic techniques are commonly used to treat dental intrusions, in the case of extrusive and lateral luxation injuries, they are less frequently used and the orthodontic approach is generally confined to the stabilization phase. Among the various possible pulp consequences, many authors consider only pulp canal obliteration (PCO) and pulp necrosis (PN), often tending to overlook physiological healing (pulp survival) and the possible development of PN after PCO. There is therefore a clear need for new, high-quality clinical studies of this topic based on systematic and standardized data collection.