###### Abstract  
The present review aims to analyze the application of infrared thermal imaging, aided by bio-heat models, as a tool for the diagnosis of skin and breast cancers. The state of the art of the related technical procedures, bio-heat transfer modeling, and thermogram post-processing methods is comprehensively reviewed. Once the thermal signatures of different malignant diseases are described, the updated thermographic techniques (steady-state and dynamic) used for cancer diagnosis are discussed in detail, along with the recommended best practices to ensure the most significant thermal contrast observable between the cancerous and healthy tissues. Regarding the dynamic techniques, particular emphasis is placed on innovative methods, such as lock-in thermography, thermal wave imaging, and rotational breast thermography. Forward and inverse modeling techniques for the bio-heat transfer in skin and breast tissues, supporting the thermographic examination and providing accurate data for training artificial intelligence (AI) algorithms, are reported with a special focus on real breast geometry-based 3D models. In terms of inverse techniques, different data processing algorithms to retrieve thermophysical parameters and growth features of tumor lesions are mentioned. Post-processing of infrared images is also described, citing both conventional processing procedures and applications of AI algorithms for tumor detection. bio-heat transfer; infrared thermal imaging; inverse modeling; steady-state and dynamic thermography; post-processing images; skin cancer; breast cancer +
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relatively high costs [5]. Developing new, accurate, objective, and early diagnostic tools is essential not only to overcome these limitations but also to avoid unnecessary biopsies and consequently reduce the costs of national health-care systems. Infrared (IR) thermography is one of the most promising technologies now available for the early detection of malignant diseases (such as skin and breast cancers). Its significant strengths are the absence of contact and dangerous radiation; it is also a non-invasive and cost-effective technique. It is based on identifying abnormal thermal patterns on the observed skin surface when compared to the healthy region, as they are recognized as biological risk markers [6]. Surprisingly, the first applications of IR thermography to diagnose breast cancers and melanomas date back to 1956 [7] and 1969 [8], respectively. However, when the observed differences between thermal patterns of cancerous and healthy tissues were subtle, this methodology showed drawbacks and limits due to poor resolution and the scan time of the first IR cameras. Moreover, the absence of standardized measurement procedures and the lack of clinicians adequately trained in the use of IR cameras represented other obstacles to the development of such a methodology. Because of these problems, IR thermography did not become popular as a diagnostic tool [6; 9; 10; 11; 12], although in 1982, it was approved as an adjunctive tool for the diagnosis of breast cancer by the Food and Drug Administration in the USA [5]. Later in the 2000s, the performance of IR cameras was significantly improved thanks to the introduction of high-sensitivity uncooled IR detectors (known as focal plane arrays), allowing less pronounced surface temperature variations to be detected. As a consequence of the improvement in IR cameras' performance along with the increasing computational capability (crucial for both realistic models and artificial intelligence algorithms), IR thermography has gained a renewed interest as a diagnostic tool. Furthermore, the increasing computational capability allows for more accurate numerical models, which are able to predict the complex relationship between surface thermal patterns and the underlying pathophysiological conditions, to be implemented and used both as support for thermographic examination and to provide reliable data useful for training artificial intelligence algorithms.