  Parameterized telescoping (including telescoping and creative telescoping)
and refined versions of it play a central role in the research area of symbolic
summation. Karr introduced 1981 $\Pi\Sigma$-fields, a general class of
difference fields, that enables one to consider this problem for indefinite
nested sums and products covering as special cases, e.g., the
($q$--)hypergeometric case and their mixed versions. This survey article
presents the available algorithms in the framework of $\Pi\Sigma$-extensions
and elaborates new results concerning efficiency.
