Transition metal dichalcogenides (TMDs) are quasi-two-dimensional layered compounds that exhibit strongly competing effects of charge-density wave (CDW) formation and superconductivity (SC). The weak van der Waals interlayer bonding between hexagonal layers of octahedral or trigonal prismatic TMD building blocks allows many polytypes to form. In the single layer 1T polytype materials, one or more CDW states can form, but the pristine TMDs are not superconducting. The 2H polytypes have two or more Fermi surfaces and saddle bands, allowing for dual orderings, which can be coexisting CDW and SC orderings, two SC gaps as in MgB2, two CDW gaps, and possibly even pseudogaps above the onset TCDWs of CDW orderings. Higher order polytypes allow for multiple CDW gaps and at least one superconducting gap. The CDW transitions TCDWs usually greatly exceed the superconducting transitions at their low Tc values, their orbital order parameters (OPs) are generally highly anisotropic and can even contain nodes, and the SC OPs can be greatly affected by their simultaneous presence. The properties of the CDWs ubiquitously seen in TMDs are remarkably similar to those of the pseudogaps seen in the high-Tc cuprates. In 2H-NbSe2, for example, the CDW renders its general s-wave SC OP orbital symmetry to be highly anisotropic and strongly reduces its Josephson coupling strength (IcRn) with the conventional SC, Pb. Hence, the pristine TMDs are highly "unconventional" in comparison with Pb, but are much more "conventional" than are the ferromagnetic superconductors such as URhGe. Applied pressure and intercalation generally suppress the TMD CDWs, allowing for enhanced SC formation, even in the 1T polytype materials. The misfit intercalation compound (LaSe)1.14(NbSe2) and many 2H-TMDs intercalated with organic Lewis base molecules, such as TaS2(pyridine) 1/2 , have completely incoherent c-axis transport, dimensional-crossover effects, and behave as stacks of intrinsic Josephson junctions. Except for the anomalously large apparent violation of the Pauli limit of the upper critical field of (LaSe)1.14(NbSe2), these normal state and superconducting properties of these intercalation compounds are very similar to those seen in the high-Tc superconductor, Bi2Sr2CaCu2O 8+δ and in the organic layered superconductor, κ-(ET)2Cu[N(CN)2]Br, where ET is bis(ethylenedithio)tetrathiafulvalene. Electrolytic intercalation of TMDs with water and metallic ions leads to compounds with very similar properties to cobaltates such as NaxCoO2 · yH2O.