Tourette syndrome (TS) is a disabling neuropsychiatric disorder characterised by persistent motor and vocal tics. TS is a highly comorbid state, hence, patients might experience anxiety, obsessions, compulsions, sleep abnormalities, depression, emotional liability, learning problems, and attention deficits in addition to tics. In spite of its complex heterogeneous genetic aetiology, recent studies highlighted a strong link between TS and genetic lesions in the HDC (L-histidine decarboxylase) gene, which encodes the enzyme that synthetises histamine, and the SLITRK1 (SLIT and TRK-like family member 1) gene, which encodes a transmembrane protein that was found to regulate neurite outgrowth. In addition to validating the contribution of a specific genetic aberration to the development of a particular pathology, animal models are crucial to dissect the function of disease-linked proteins, expose disease pathways through examination of genetic modifiers and discover as well as assess therapeutic strategies. Mice with a knockout of either Hdc or Slitrk1 exhibit anxiety and those lacking Hdc, display dopamine agonist-triggered stereotypic movements. However, the mouse knockouts do not spontaneously display tics, which are recognised as the hallmark of TS. In this review, we explore the features of the present genetic animal models of TS and identify reasons for their poor resemblance to the human condition. Importantly, we highlight ways forward aimed at developing a valuable genetic model of TS or a model that has good predictive validity in developing therapeutic drugs for the treatment of tics, hence potentially accelerating the arduous journey from lab to clinic.