Application of machine learning is currently one of the hottest topics in the fluid mechanics field. While machine learning seems to have a great possibility, its limitations should also be clarified. In our research group, we have started a research project to construct a nonlinear feature extraction method by applying machine learning techniques to big data of fluid flow, i.e., extracting the low-dimensional nonlinear modes essential to the unsteady flow phenomena and deriving the governing equations for such low-dimensionalized dynamics. This self-review article is a focused but extended version of the keynote lecture given by the author at the 7th International Conference on Jets, Wakes and Separated Flows (ICJWSF2022). We will first introduce the use of a convolutional neural network (CNN) to learn the temporal evolution of cross-sectional velocity field in a turbulent channel flow. Subsequently, we also consider an application of CNN for extraction of low-dimensional dynamics for flow around a bluff body accompanying vortex shedding and our preliminary attempt to use the extracted low-dimensional dynamics for an advanced design of flow control.