Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals heterosructures with a focus on heterobilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those heterobilayers are introduced. Most recent findings focusing on different transition metal dichalcogenides heterostructures are presented and possible optical transitions between different valleys, appearance of moire patterns and signatures of moire excitons are discussed. The fascinating and fast growing research on van der Waals hetero-bilayers provide promising insights required for their application as emerging quantum-nano materials.
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