While there has been a surge in interest over the past two decades in quantitative and computational approaches to questions in historical linguistics, this research program has focused on human languages in only one of the two main modalities, that is, spoken languages in the aural-oral modality. Signed languages in the visual-gestural modality, in contrast, have been largely absent from theoretical discussions concerning the evolution of language and from methodological discussions aimed at developing infrastructures for data sharing and data accessibility in historical comparative research. In this presentation, we highlight two of the main obstacles to quantitative and computational approaches in historical comparative research on sign languages. These obstacles include the lack of consensus among researchers on a sign language transcription system or on alternative, computer-readable representations of signs. The lack of consensus in data representation schemes has direct consequences for the accessibility of historical comparative data, for the reproducibility of comparative studies, and for data sharing among historical linguists. A second main obstacle to quantitative approaches in sign language historical research relates to models of diachronic change in signed languages. While most quantitative, computational approaches to historical research on spoken languages depend on the prior application of the comparative method for identifying cognate vocabulary (Gray & Atkinson 2003, Gray et al 2009, Sagart et al 2019), sign scholars have yet to successfully apply the comparative method to identify recurring correspondences across putatively cognate signs (Power et al 2019, Power 2020); and it remains unclear whether the regularity principle —- a foundational assumption of the comparative method (Rankin 2008, Hale 2015) -— holds for signed languages. How should sign scholars approach the comparison and validation of models of sign change while lacking a gold standard arrived at by independent methods? In the final part of this presentation, we introduce the Sign Change project, a new research initiative aimed at exploring the theoretical and methodological foundations of sign language historical linguistics, with a focus on thirteen sign languages in two putative families, the French and BANZSL families.