Until now, only two intrinsically two-dimensional materials have been isolated: graphene and boron nitride (BN). As a consequence, the knowledge of two-dimensional systems is still limited and other classes of two-dimensional materials are needed to enrich our understanding of these systems. In this thesis, we studied the structural and mechanical properties of two-dimensional transition metal dichalcogenide (TMD) crystals. Apart from fundamental interest, transition metal dichalcogenides have great appeal due to their possible applications in electronic. Here, the focus is on MoS2, while the main employed techniques are transmission electron microscopy and nano-indentation. The thesis is divided into three parts. The first part is devoted to summarize the general properties of transition metal dichalcogenide materials, to illustrate the instrumentation, and to describe the deposition techniques used in sample preparation. In particular, the transfer technique used to transfer selected flakes among different substrates is described. In the second part, we investigate single-layer MoS2 flakes obtained by mechanical exfoliation. We describe two methods to distinguish single-layer MoS2 flakes from thicker ones by electron diffraction. Ripples are observed over the flake surface. Thanks to diffraction pattern interpretation and high resolution transmission electron microscopy, their amplitude is estimated to be 0.6 - 1 nm in height. Nano-indentation is used to determine the Young’s modulus and the breaking strength of single-layer MoS2 membranes. The Young’s modulus is EY =270±100GPa while the breaking strength is σmax =23±5 GPa. In order to fully take advantage of the promising electronic properties of transition metal dichalcogenide, it is necessary to grow them over large scale. In this way, the pla- nar technology developed for silicon can be implemented and a large number of devices with uniform electrical properties can be realized. When comparing different growths, methods to quantify the quality of the films are mandatory. In this context, we show that transmission electron microscopy is a valuable method to characterize large area MoS2 and MoSe2 films. We are able to estimate the grain size and to have a direct view of the grain boundaries. In fact, grain size and boundary quality constitute the important parameters to qualify two-dimensional poly-crystalline films. Finally, we describe a novel in-situ experiment which allows us to simultaneously perform transmission electron microscopy and electrical characterization on a device based on a suspended MoS2 flakes. The effect of the current flow on the MoS2 flake are considered. These two topic constitute the last part of the thesis.