Attempts to understand the mechanism of unconventional superconductivity in the high-Tc cuprates have been at best partially successful, in part due to what makes them so interesting, their high Tc. Though rather substantial evidence points to d-wave pairing that possibly is mediated by spin fluctuations, phonons also contribute to physical properties at temperatures of order 40 to 150 K where superconductivity develops. The simultaneous presence of spin-fluctuations and phonons, not to mention possible proximity to a quantum-critical point and issues of inhomogeneous charge distributions, have made the cuprates particularly challenging to understand. Progress might be possible, however, if rather simpler analogues to the cuprates were available. A new family of compounds, with chemical composition CeMIn5 (M=Rh, Co and Ir), may represent the desired analogues. Like the cuprates, they crystallize in a layered structure and exhibit hallmarks of d-wave superconductivity mediated by antiferromagnetic spin fluctuations. Though their superconducting transition temperatures are rather low, less than 2.3K, compared to the cuprates, they are very high for Ce-based superconductors. These 'high-Tc's appear to be related to the layered structure and proximity to a quantum-critical point. Besides possibly being heavy-fermion analogues of the cuprates, these new compounds also show several fascinating features that deserve further attention.