Was the Counter-Reformation a reaction to Luther, or a Catholic reform of its own?

It was both, and historians still argue about the proportions. The Counter-Reformation, also called the Catholic Revival or Catholic Reformation, was the period of Catholic resurgence initiated in response to and as an alternative to, or from similar insights as, the Protestant Reformation. It was a comprehensive effort arising from the decrees of the Council of Trent, which met from 1545 to 1563 and is frequently taken as the starting point.

At Trent the Church said no to compromise with Protestants. The council rejected all compromise, upheld salvation through grace by faith and the works of that faith, not faith alone, and reaffirmed transubstantiation and the seven sacraments. Yet Pope Paul III had also tasked it with institutional reform, from corrupt bishops and priests to the sale of indulgences. Many rural priests were poorly educated and often did not know Latin, so parish priests were to be better educated in theology. Trent also combated absenteeism, bishops living in Rome or on estates rather than in their dioceses.

New energy came from new orders. The Jesuits, recognised in 1540, were the most effective, organized along military lines, and took part in the expansion of the Church in the Americas and Asia through missionary activity. In an era when some Protestant reformers were destroying images of saints, Catholic reformers reaffirmed the importance of art.

Now the argument. The very term "Counter-Reformation" was coined by German historians in the late eighteenth century as a negative concept for Catholic repressions. The French historian Henri Daniel-Rops insisted that the movement did not begin with Trent, long after Luther, since its origins were much earlier. The historian Massimo Firpo therefore distinguishes a general Catholic Reformation from a narrower Counter-Reformation of orthodoxy and repression.