Imaging flow cytometry combines the fluorescence sensitivity and high-throughput capabilities of flow cytometry with single-cell imaging, and hence provides high-volume data well-matched to the strengths of deep learning. We present DeepFlow, a data analysis workflow for imaging flow cytometry that combines deep convolutional neural networks with non-linear dimension reduction. DeepFlow uses learned features of the neural network to visualize, organize and biologically interpret single-cell data. Dissecting the cell cycle as a source of cell-to-cell variability is crucial for quantitative single-cell biology. We demonstrate DeepFlow for a large dataset of cell-cycling Jurkat cells. First, we reconstruct the cells' continuous progression through cell cycle from raw image data. This shows that DeepFlow can learn a continuous distance measure between categorical phenotypes. Second, we are able to detect and separate a subpopulation of dead cells, although the data set had been cleaned using established approaches. DeepFlow detects this morphologically abnormal subpopulation in an unsupervised manner. Third, in label-free classification of cell cycle phases, we reach a 6-fold reduction in error rate as compared to a recent approach based on boosting on a series of image features. In contrast to previous methods, DeepFlow's predictions are fast enough to consider integration with the imaging flow cytometry measurement process.