  In this survey we collect all results regarding the construction of the
Framization of the Temperley-Lieb algebra of type $A$ as a quotient algebra of
the Yokonuma-Hecke algebra of type $A$. More precisely, we present all three
possible quotient algebras the emerged during this construction and we discuss
their dimension, linear bases, representation theory and the necessary and
sufficient conditions for the unique Markov trace of the Yokonuma-Hecke algebra
to factor through to each one of them. Further, we present the link invariants
that are derived from each quotient algebra and we point out which quotient
algebra provides the most natural definition for a framization of the
Temperley-Lieb algebra. From the Framization of the Temperley-Lieb algebra we
obtain new one-variable invariants for oriented classical links that, when
compared to the Jones polynomial, they are not topologically equivalent since
they distinguish more pair of non isotopic oriented links. Finally, we discuss
the generalization of the newly obtained invariants to a new two-variable
invariant for oriented classical links that is stronger than the Jones
polynomial.
