In this talk we present results obtained within the MULAC project concerning the topics of invertibility
of multipliers and unconditional convergence of multipliers.

Concerning unconditional convergence of multipliers, we discuss the following:
sufficient conditions for unconditional convergence of multipliers,
necessary conditions for unconditional convergence of multipliers;
in certain cases we determine conditions which are necessary and sufficient.

Concerning invertibility of multipliers, we point on the following results:
necessary conditions for invertibility of Bessel multipliers;
sufficient conditions for invertibility of frame multipliers;
conditions which are necessary and sufficient for invertibility of Riesz multipliers;
expression for the inverse multiplier.

Then we discuss some open problems for future work.