Cervical cancer remains a significant cause of mortality in low-income countries. However, it can often be cured by removing the affected tissues when detected in early stages. Therefore, it is relevant to provide universal and efficient access to cervical screening programs, being digital colposcopy an inexpensive technique with high potential of scalability. The development of computer-aided diagnosis systems for the automated processing of digital colposcopies has gained the attention of the computer vision and machine learning communities in the last decade, giving origin to a wide diversity of tasks and computational solutions. However, there is a lack of a unified framework to discuss the main tasks and to assess their performance. Thus, in this paper, we studied the core research lines surrounding the automated analysis of digital colposcopies and built a topology of problems and techniques, including their key properties, advantages, and limitations. Also, we discussed the open challenges in the area and released a database that serves as a common basis to evaluate such systems.