An element \(a\) of a semigroup \((S,.)\) is called left (right) magnifying if there exists a proper subset \(M\) of \(S\) such that \(aM=S\) (\(Ma=S\)). \textit{K. Tolo} [Pac. J. Math. 31, 523--535 (1969; Zbl 0188.05401)] investigated the relationship between the existence of particular such elements in a semigroup \(S\) and the property of \(S\) to be factorizable, i.e. \(S=A.B\) for some proper subsemigroups \(A\), \(B\) of \(S\). Magnifying elements in semigroups with one-sided identity were also studied by \textit{V. Shvarc} and \textit{I. Jaroker} [Usp. Mat. Nauk 19, No. 4(118), 209--214 (1964; Zbl 0241.20053)]. In the paper under review the authors continue the investigation of such elements in simple and bisimple semigroups, respectively. In particular, it is shown that left magnifying elements exist 1) in a simple semigroup \(S\) with left identity iff \(S\) is not a right group, 2) in a bisimple semigroup \(S\) iff \(S\) is not a right group and contains a left identity or \(S\) is right simple and contains no idempotents, 3) in a regular semigroup \(S\) iff \(S\) admits a left identity \(e\) and an element \(t\in S\) such that \(tS=S\), \(te=t\) and \(e\notin St\). Finally, it is proved that every left (right) magnifying element of a semigroup \(S\) is maximal in the natural partial order of \(S\) [see the reviewer, Proc. Am. Math. Soc. 97, 384--388 (1986; Zbl 0596.06015)].