Spiritual gifts and their exercise within today's Catholic Church Regarding the apostle Paul's discussion of spiritual gifts (τὰ πνευματικὰ χαρίσματα) in 1 Corinthians 12-14, he uses the words ".....when you come together" (1 Cor. 14:26). Is he referring to the exercise and manifestation of spiritual gifts within the celebration of the Eucharist during his time? If so, should these gifts be exercised in today's Eucharistic celebrations, and if so, how? Perhaps the apostle is citing the exercise of these gifts within a different context (e.g., the Agape which preceded the Eucharist - more akin to a "charismatic prayer group" outside the Mass). 

What does the Catholic Church teach on this matter? Have these gifts (prophecy, tongues, interpretation, etc.) ceased, or are they still of great value today within the Church?
I'm only a novice, but I have been researching this subject lately and I would be happy to provide you with what little insight I can.

Different Catholic churches will have different positions on cessation vs continuation.

Typically Catholic churches hold a view point of cessation, however, Pope Francis in particular has been increasingly accepting of Charismatic Catholics (the word "Charismatic" here is implying that they believe in the gifts from 1 Corinthians) and he has invited them to the upcoming jubilee.

http://georgiabulletin.org/news/2014/06/pope-invites-charismatics-vatican-2017-jubilee/

https://en.wikipedia.org/wiki/Catholic_Charismatic_Renewal

Hope it helps!