Over the last decade, supervised deep learning on manually annotated big data has been progressing significantly on computer vision tasks. But the application of deep learning in medical image analysis was limited by the scarcity of high-quality annotated medical imaging data. An emerging solution is self-supervised learning (SSL), among which contrastive SSL is the most successful approach to rivalling or outperforming supervised learning. This review investigates several state-of-the-art contrastive SSL algorithms originally on natural images as well as their adaptations for medical images, and concludes by discussing recent advances, current limitations, and future directions in applying contrastive SSL in the medical domain.