Retinal fundus photographs can be used to detect a range of retinal conditions. Here we show that deep-learning models trained instead on external photographs of the eyes can be used to detect diabetic retinopathy (DR), diabetic macular oedema and poor blood glucose control. We developed the models using eye photographs from 145,832 patients with diabetes from 301 DR screening sites and evaluated the models on four tasks and four validation datasets with a total of 48,644 patients from 198 additional screening sites. For all four tasks, the predictive performance of the deep-learning models was significantly higher than the performance of logistic regression models using self-reported demographic and medical history data, and the predictions generalized to patients with dilated pupils, to patients from a different DR screening programme and to a general eye care programme that included diabetics and non-diabetics. We also explored the use of the deep-learning models for the detection of elevated lipid levels. The utility of external eye photographs for the diagnosis and management of diseases should be further validated with images from different cameras and patient populations.