Since the first observation of ultrafast demagnetization in Ni thin films by Beaurepaire et al 20 years ago, understanding the interaction between ultrashort laser pulses and magnetization has become a topic of huge interest. In 2007, an intriguing discovery related to ultrafast demagnetization was the observation of all-optical switching (AOS) of magnetization in ferrimagnetic GdFeCo alloy films using only femtosecond laser pulses. This review discusses the recent studies elucidating several key issues regarding the all-optical switching phenomenon. Although AOS had long been restricted to GdFeCo alloys, it turned out to be a more general phenomenon for a variety of ferrimagnetic as well as ferromagnetic materials. This discovery helped pave the way for the integration of all-optical writing in data storage industries. Nevertheless, theoretical models explaining the switching in GdFeCo alloy films do not appear to apply in the other materials, thus questioning the uniqueness of the microscopic origin of all-optical switching. By investigating the integration of all-optical switching in spintronic devices, two types of all-optical switching mechanism have been distinguished: a single-pulse heat-only switching in ferrimagnetic GdFeCo alloys, and a two regime helicity-dependent switching in both ferrimagnetic TbCo alloys and ferromagnetic Co/Pt multilayers. Another key issue discussed in this review is the necessary condition for the observation of all-optical switching. Many models have been proposed but are strongly challenged by the discovery of such switching in ferromagnets. A comprehensive investigation of the magnetic parameters governing all-optical switching demonstrate that its observation requires magnetic domains larger than the laser spot size during the cooling process; such a criterion is common for both ferri- and ferro-magnets. These investigations strongly improve our understanding and give intriguing insights into the rich physics of the ultrafast manipulation of magnetic order.