The potential of nailfold capillaroscopy to contribute to early diagnosis of systemic sclerosis was recognised over 50 years ago, and abnormal nailfold capillaries form part of the international classification criteria for the disease. Despite this, capillaroscopy is often not used in clinical practice, because interpretation of nailfold images is challenging and subjective. We review the large body of work that has sought to replace or augment subjective judgement with objective measurement, covering both fully-quantitative and semi-quantitative approaches. This corpus laid the foundations for fully-automated quantitative capillaroscopy systems that have come of age with the emergence of sophisticated artificial intelligence algorithms. We review previous work on automation and describe two state-of-the-art systems, discussing their strengths and weaknesses and identifying future challenges for the field.