Background: The use of digital tools to measure physiological and behavioural variables of potential relevance to mental health is a growing field sitting at the intersection between computer science, engineering and clinical science. We aim to summarise the literature on remote measuring technologies, mapping methodological challenges and threats to reproducibility, and to identify leading digital signals for depression. Methods: Medical and computer science databases were searched between January 2007 to November 2019. Published studies linking depression and objective behavioural data obtained from smartphone and wearable device sensors in adults with unipolar depression and healthy subjects were included (PROSPERO registration: 2019 CRD42019159929). A descriptive approach was taken to synthesise study methodologies. Results We included 52 studies and found threats to reproducibility and transparency arising from failure to provide comprehensive descriptions of recruitment strategies, sample information, feature construction and the determination and handling of missing data. The literature is characterised by small sample sizes, short follow-up duration and great variability in quality of reporting, limiting the interpretability of pooled results. Bivariate analyses show some consistency in statistically significant associations between depression and digital features from sleep, physical activity, location, and phone use data. Regression and classification machine learning models found predictive value of aggregated features. Interpretation: Recommendations are put forward to improve aspects of generalisability and reproducibility, such as wider diversity of samples, thorough reporting methodology and the potential for reporting bias in studies with numerous features. Funding: National Institute for Health Research (NIHR) Biomedical Research Centre at South London and Maudsley NHS Foundation Trust and King's College London.