The high-throughput extraction of quantitative information from medical images, known as radiomics, has grown in interest due to the current necessity to quantitatively characterize tumour heterogeneity. In this context, texture analysis, consisting of a variety of mathematical techniques that can describe the grey-level patterns of an image, plays an important role in assessing the spatial organization of different tissues and organs. For these reasons, the potentiality of texture analysis in the context of radiotherapy has been widely investigated in several studies, especially for the prediction of the treatment response of tumour and normal tissues. Nonetheless, many different factors can affect the robustness, reproducibility and reliability of textural features, thus limiting the impact of this technique. In this review, an overview of the most recent works that have applied texture analysis in the context of radiotherapy is presented, with particular focus on the assessment of tumour and tissue response to radiations. Preliminary, the main factors that have an influence on features estimation are discussed, highlighting the need of more standardized image acquisition and reconstruction protocols and more accurate methods for region of interest identification. Despite all these limitations, texture analysis is increasingly demonstrating its ability to improve the characterization of intratumour heterogeneity and the prediction of clinical outcome, although prospective studies and clinical trials are required to draw a more complete picture of the full potential of this technique.