As structural analogues of graphene but with a sizeable band gap, monolayers of group-VIB transition metal dichalcogenides (MX2, M = Mo, W; X = S, Se, Te, etc.) have emerged as the ideal two dimensional prototype for exploring fundamental issues in physics such as valley polarization, and for engineering a wide range of nanoelectronic, optoelectronic and photocatalytic applications. Recently, chemical vapour deposition (CVD) was introduced as a more efficient preparation method than traditional chemical or physical exfoliation options, and has allowed for the successful synthesis of large-area MX2 monolayers possessing a large domain size, high thickness uniformity and continuity, and satisfactory crystal quality. This tutorial review therefore focuses on introducing the more recent advances in the CVD growth of MX2 (MoS2, WS2, MoS2(1-x)Se2xetc.) monolayers via the sulphurisation/decomposition of pre-deposited metal-based precursors, or the one-step reaction and deposition of gaseous metal and chalcogen feedstocks. Differences in growth behaviour caused by commonly used amorphous SiO2/Si, and newly adopted insulating single crystal substrates such as sapphire, mica and SrTiO3, are also comparatively presented. Also discussed are the essential parameters that influence the growth of MX2, such as the temperature, the source-substrate distance and the composition of the carrier gas (Ar/H2). Finally, an assessment is provided for viable future pathways for fine-tuning of the domain size and orientation, thickness uniformity, and the bandgap of MX2 and its alloys.