The Azusa Street revival that began in Los Angeles in 1906 put continuing prophecy, healing and tongues at the public center of a Christian movement in a way earlier Holiness revivals had not, and the Pentecostal denominations that grew from it, the Assemblies of God among the largest, built continuationism into their statements of faith as a settled conviction rather than an open question.
The Charismatic movement of the 1960s and 1970s carried the same conviction into Catholic parishes and mainline Protestant congregations that had no Pentecostal background at all, producing Catholic Charismatic Renewal and charismatic wings inside Anglican, Lutheran and other historically cessationist-leaning or simply gift-silent traditions. A further wave in the 1980s, often called the Third Wave, brought continuationist practice, expectant prayer for healing and prophetic ministry particularly, into evangelical churches that kept a more traditional, non-Pentecostal style of worship otherwise.
The cumulative effect has been to make continuationism, in practice if not always in official confession, the working assumption of a large and growing share of global Christianity, concentrated most heavily in the Pentecostal and Charismatic movements themselves but no longer confined to denominations that use either word in their name.