In this review, typical clinical complications involving periodontal tissues are illustrated that can be encountered in conjunction with orthodontic therapy (OT). Special considerations are given for various clinical scenarios, such as the patient presenting in periodontal health, with periodontitis, or with mucogingival conditions. While some of the complications are seen as common side effects of OT, other, more severe, problems that could have been avoided may be viewed as treatment errors. Recommendations are made on how to prevent these complications, based on the currently available evidence, on clinical practice guidelines, and on expert opinion. In conclusion, while there are several areas in which OT can have unwanted adverse effects on periodontal/mucogingival conditions, there is also great potential for synergies, offering opportunities for close cooperation between the two specialties (periodontics and orthodontics) for the benefit of patients affected by tooth malpositioning and/or periodontal or mucogingival problems.