Neuromorphic Engineering has emerged as an exciting research area, primarily owing to the paradigm shift from conventional computing architectures to data-driven, cognitive computing. There is a diversity of work in the literature pertaining to neuromorphic systems, devices and circuits. This review looks at recent trends in neuromorphic engineering and its sub-domains, with an attempt to identify key research directions that would assume significance in the future. We hope that this review would serve as a handy reference to both beginners and experts, and provide a glimpse into the broad spectrum of applications of neuromorphic hardware and algorithms. Our survey indicates that neuromorphic engineering holds a promising future, particularly with growing data volumes, and the imminent need for intelligent, versatile computing.