Monolayers of transition metal dichalcogenides (TMDs), such as MoS2 and WS2, have recently triggered worldwide research interest due to their remarkable optical and electronic properties. More fascinatingly is the fact that these monolayers could also adopt various morphologies with exposed edges that include triangular, hexagonal or star-shaped clusters, in addition to nanoribbons. Exciting progress has been recently achieved in the synthesis, characterization, device fabrication and functionalization of these monolayer and few-layer TMDs. This article firstly reviews the properties of bulk and monolayer/few-layer TMDs. The "top-down" and "bottom-up" synthesis routes for different TMDs are then summarized. Raman spectroscopy is now becoming a key tool used to characterize atomically thin TMDs, and this review will show the latest advances using this spectroscopic technique. Here we also summarize the most relevant characterization techniques, optical/electronic device fabrication, functionalization and defect engineering of TMDs. There are numerous opportunities for applications and multiple challenges to overcome, and this review will be instructive and useful to researchers working in the area of 2-dimensional materials, as well as scientists and engineers interested in their applications in electronics, optics, catalysis, energy and many others. (C) 2015 Elsevier Ltd. All rights reserved.