  In this note, we survey some recent developments in birational geometry
concerning the boundedness of algebraic varieties. We delineate a strategy to
extend some of these results to the case of generalized pairs, first introduced
by Birkar and Zhang, when the associated log canonical divisor is ample, and
the volume is fixed. In this context, we show a version of deformation
invariance of plurigenera for generalized pairs. We conclude by discussing an
application to the boundedness of varieties of Kodaira dimension
$\kappa(X)=\dim(X)-1$.
