  Transition metal dichalcogenides (TMDs) are quasi-two-dimensional layered
compounds exhibiting strongly competing charge-density wave (CDW) and
superconducting (SC) order parameters (OPs). The weak van der Waals interlayer
bonding between hexagonal layers of octahedral or trigonal prismatic TMD
building blocks allows for many polytypes. The non-superconducting $1T$
polytypes can have one or more CDWs. 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 MgB$_2$, or two CDW gaps. The CDW
transitions $T_{\rm CDW}$s usually greatly exceed the low superconducting
$T_{\rm c}$s, their orbital OPs are generally highly anisotropic and can even
contain nodes, are remarkably similar to the the high-$T_{\rm c}$ cuprate
pseudogaps, and the SC OPs can be greatly affected by their presence. In
2$H$-NbSe$_2$, the CDW renders its general $s$-wave SC OP orbital symmetry to
be highly anisotropic and strongly reduces its Josephson coupling strength
($I_{\rm c}R_{\rm n}$) with Pb. Pressure and intercalation generally suppress
the CDWs, enhancing $T_{\rm c}$. The misfit intercalation compound
(LaSe)$_{1.14}$(NbSe$_2$) and many intercalated $2H$-TMDs, such as
TaS$_2$(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 violation of the Pauli limit of the
upper critical field of (LaSe)$_{1.14}$(NbSe$_2$), these properties are very
similar to those of the cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and of the
organic layered superconductor, $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br. Intercalates
of TMDs with water and metallic ions are very similar to Na$_x$CoO$_2\cdot
y$H$_2$O.
