  We discuss in detail the pulsation properties of variable stars in globular
clusters (GCs) and in Local Group (LG) dwarf galaxies. Data available in the
literature strongly support the evidence that we still lack a complete census
of variable stars in these stellar systems. This selection bias is even more
severe for small-amplitude variables such as Oscillating Blue Stragglers (OBSs)
and new exotic groups of variable stars located in crowded cluster regions. The
same outcome applies to large-amplitude, long-period variables as well as to RR
Lyrae and Anomalous Cepheids in dwarf galaxies.
