The rapid technological development in the past decades has significantly increased the amount of available data in the world. Naturally, models that scale with the size of the available data, such as Deep Neural Networks, have become the primary strategy for several research fields with abundant data (e.g., computer vision and natural language processing). With this large data availability, research on learning models that can adapt incrementally to continual streams of data has been encouraged. In this way, the field of Continual Learning proposes to study the ability to learn consecutive tasks without losing performance on the previously trained ones. In computer vision, researchers have mainly focused their efforts on incremental classification tasks, but continual object detection also deserves attention due to its vast range of applications in robotics and autonomous vehicles. In fact, this scenario is even more complex than conventional classification, given the occurrence of instances of classes that are unknown at the time but can appear in subsequent tasks as a new class to be learned, resulting in missing annotations and conflicts with the background label. Since this field is in its early stages, research in continual object detection still offers several opportunities and lacks methodology conventions. This Ph.D. thesis investigates the field more thoroughly and identifies possible links with related areas such as general continual learning and neural network pruning. Specifically, we proposed the first systematic review on the topic, developed two metrics for improving the analysis of performance in incremental detection scenarios, investigated which exemplar selection method works best for replay-based continual detection strategies, and explored different ways to identify and penalize important task parameters across sequential updates. To validate our proposals and claims, we conducted experiments and reported results comparable to the current state-of-the-art in popular detection benchmarks (i.e., PASCAL VOC) adapted to the incremental setting, as well as in real-world datasets and applications. The findings presented in this thesis were also put into practice in two applications. Firstly, they were tested in the 3 rd CLVISION Challenge, where we were able to achieve the 3 rd place in the continual instance detection track. Secondly, they were applied to the continual aerial inspection of transmission towers at TAESA, the largest Brazilian electric power transmission company, to improve the automation of their inspection pipeline.