Breast cancer is a common fatal disease for women. Early diagnosis and detection is necessary in order to improve the prognosis of breast cancer affected people. For predicting breast cancer, several automated systems are already developed using different medical imaging modalities. This paper provides a systematic review of the literature on artificial neural network (ANN) based models for the diagnosis of breast cancer via mammography. The advantages and limitations of different ANN models including spiking neural network (SNN), deep belief network (DBN), convolutional neural network (CNN), multilayer neural network (MLNN), stacked autoencoders (SAE), and stacked de-noising autoencoders (SDAE) are described in this review. The review also shows that the studies related to breast cancer detection applied different deep learning models to a number of publicly available datasets. For comparing the performance of the models, different metrics such as accuracy, precision, recall, etc. were used in the existing studies. It is found that the best performance was achieved by residual neural network (ResNet)-50 and ResNet-101 models of CNN algorithm.