Brain-inspired computer vision aims to learn from biological systems to develop advanced image processing techniques. However, its progress so far is not impressing. We recognize that a main obstacle comes from that the current paradigm for brain-inspired computer vision has not captured the fundamental nature of biological vision, i.e., the biological vision is targeted for processing spatio-temporal patterns. Recently, a new paradigm for developing brain-inspired computer vision is emerging, which emphasizes on the spatio-temporal nature of visual signals and the brain-inspired models for processing this type of data. In this paper, we review some recent primary works towards this new paradigm, including the development of spike cameras which acquire spiking signals directly from visual scenes, and the development of computational models learned from neural systems that are specialized to process spatio-temporal patterns, including models for object detection, tracking, and recognition. We also discuss about the future directions to improve the paradigm.