The Latin language is far from being extinct even though you only hear it at times in Church. Our common experience today at Mass prayed in the Ordinary Forum is often in the language of the people. The official language of the Catholic Church, however, remains Latin: the texts of the church, the texts of the pope, and importantly, in the prayer of the Church. Fear not. The "house" language today, the daily work of the curia is Italian. It is possible that at some point English will replace Italian.
The Carmelite friar Father Reginald Foster is the renown contemporary father of the Latin language. He spent several decades in Rome working, teaching and writing in Latin. Now he's retired from active teaching but he keeps his hands in the field by consulting, developing teaching materials, writing and attending some initiatives. One of his works is Corpus Latinitatis.
A recent Reuters article brings to life in a brief fashion the influence of Father Reg in "Spreading the word that Latin lives..."