Software as a Service has been around for a while. In its early years—late 1990s-early 2000s—it was mostly aimed at individual and departmental use, but in more recent years SaaS has been deployed at the enterprise level. There are companies that don’t use anything else.
In the beginning, SaaS was used by companies more for productivity applications like web conferencing, managing travel expenses and sales contacts, or time-tracking than for core business applications.