Existing computational approaches have not yet resulted in effective and efficient computer-aided tools that are used in pathologists' daily practice. Focusing on a computer-based qualification for breast cancer diagnosis, the present study proposes two deep learning architectures to efficiently and effectively detect and classify mitosis in a histopathological tissue sample. The first method consists of two parts, entailing a preprocessing of the digital histological image and a free-handcrafted-feature Convolutional Neural Network (CNN) used for binary classification. Results show that the methodology proposed can achieve $95\%$ accuracy in testing, with an F1-score of $94.35\%$. This result is higher than the results using classical image processing techniques and also higher than the approaches combining CCNs with handcrafted features. The second approach is an end-to-end methodology using semantic segmentation. Results showed that this algorithm can achieve an accuracy higher than $95\%$ in testing and an average Dice index of $0.6$, higher than the existing results using CNNs ($0.9$ F1-score). Additionally, due to the semantic properties of the deep learning approach, an end-to-end deep learning framework is viable to perform both tasks: detection and classification of mitosis. The results show the potential of deep learning in the analysis of Whole Slide Images (WSI) and its integration to computer-aided systems. The extension of this work to whole slide images is also addressed in the last sections; as well as, some computational key points that are useful when constructing a computer-aided-system inspired by the proposed technology.