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Rare earth elements are generally called as

$\begin {array} {1 1} Lanthanides \\ Actinides \\ Alkali \;metals \\Alkaline\;metals \end {array}$

Lanthanides [rare-fleries-first inner transition]$\rightarrow 6^{th}$ period.
As defined by IUPAC, a rare earth element (REE) or rare earth metal is one of a set of seventeen chemical elements in the periodic table, specifically the fifteen lanthanides plus scandium and yttrium.
edited Aug 1, 2014