Imaging biomarkers derived from MRI or CT describe functional properties of tumours and normal tissues. They are finding increasing numbers of applications in diagnosis, monitoring of response to treatment and assessment of progression or recurrence. Imaging biomarkers also provide scope for assessment of heterogeneity within and between lesions. A wide variety of functional parameters have been investigated for use as biomarkers in oncology. Some imaging techniques are used routinely in clinical applications while others are currently restricted to clinical trials or preclinical studies. Apparent diffusion coefficient, magnetization transfer ratio and native T1 relaxation time provide information about structure and organization of tissues. Vascular properties may be described using parameters derived from dynamic contrast-enhanced MRI, dynamic contrast-enhanced CT, transverse relaxation rate (R2*), vessel size index and relative blood volume, while magnetic resonance spectroscopy may be used to probe the metabolic profile of tumours. This review describes the mechanisms of contrast underpinning each technique and the technical requirements for robust and reproducible imaging. The current status of each biomarker is described in terms of its validation, qualification and clinical applications, followed by a discussion of the current limitations and future perspectives.