Optical coherence tomography (OCT) is a non-contact method for imaging the topological and internal microstructure of samples in three dimensions. OCT can be configured as a conventional microscope, as an ophthalmic scanner, or using endoscopes and small diameter catheters for accessing internal biological organs. In this Primer, we describe the principles underpinning the different instrument configurations that are tailored to distinct imaging applications and explain the origin of signal, based on light scattering and propagation. Although OCT has been used for imaging inanimate objects, we focus our discussion on biological and medical imaging. We examine the signal processing methods and algorithms that make OCT exquisitely sensitive to reflections as weak as just a few photons and that reveal functional information in addition to structure. Image processing, display and interpretation, which are all critical for effective biomedical imaging, are discussed in the context of specific applications. Finally, we consider image artifacts and limitations that commonly arise and reflect on future advances and opportunities.