Histology images are extensively used by pathologists to assess abnormalities and detect malignancy in breast tissues. On the other hand, Convolutional Neural Networks (CNN) are by far, the privileged models for image classification and interpretation. Based on these two facts, we surveyed the recent CNN-based methods for breast cancer histology image analysis. The survey focuses on two major issues usually faced by CNN-based methods namely the design of an appropriate CNN architecture and the lack of a sufficient labelled dataset for training the model. Regarding the design of the CNN architecture, methods examining breast histology images adopt three main approaches: Designing manually from scratch the CNN architecture, using pre-trained models and adopting an automatic architecture design. Methods addressing the lack of labelled datasets are grouped into four categories: methods using pre-trained models, methods using data augmentation, methods adopting weakly supervised learning and those adopting feedforward filter learning. Research works from each category and reported performance are presented in this paper. We conclude the paper by indicating some future research directions related to the analysis of histology images.