Sacred Scripture clearly speaks of a need for fasting.
"Yet even now, says the Lord, return to me with all your heart, with fasting, with weeping, and with mourning" (Joel 2, 12);
"Prayer is good when accompanied by fasting, almsgiving, and righteousness" (Tob. 12, 8);
"And the people of Nineveh believed God; they proclaimed a fast, and everyone, great and small, put on sackcloth" (Jon. 3, 5);
"But as for me, when they were sick, I wore sackcloth; I afflicted myself with fasting. I prayed with head bowed on my bosom" (Ps. 35 , 13);
"Then I turned to the Lord God, to seek an answer by prayer and supplication with fasting and sackcloth and ashes" (Dan. 9, 3).
Our Lord Jesus Christ Himself spoke of how and when we should fast:
"But when you fast, put oil on your head and wash your face, so that your fasting may be seen not by others but by your Father who is in secret; and your Father who sees in secret will reward you" (St. Matt. 6, 17-18);
"Jesus said to them, The wedding guests cannot fast while the bridegroom is with them...As long as they have the bridegroom with them, they cannot fast. The days will come when the bridegroom is taken away from them, and then they will fast on that day" (St. Mark 2, 19-20).
Christ Himself fasted forty days and forty nights: St. Matt. 4, 1; St. Luke 4.
Fasting has since the beginning been part of the Church's ceremonial worship:
"While they were worshiping the Lord and fasting, the Holy Spirit said, Set apart for me Barnabas and Saul for the work to which I have called them. Then after fasting and praying they laid their hands on them and sent them off" (Acts 13, 2-3);
"And after they had appointed elders for them in each church, with prayer and fasting they entrusted them to the Lord in whom they had come to believe" (Acts 14, 23).
Fasting gives added strength to the apostle against the powers of the Evil One:
"Then came the disciples to Jesus secretly, and said: Why could not we cast them out? Jesus said to them: Because of your unbelief...But this kind is not cast out but by prayer and fasting" (St. Matt. 17, 17-20 [Douai]). " I chastice my body and bring it into subjections, lest perhaps after having preached to others, I should become a castaway". - 1 Corinth 9:27
Fasting is a sign of the suffering and penitential Christian:
"But in all things let us exhibit ourselves as the ministers of God, in much patience, in tribulation, in necessities, in distresses, in stripes, in prisons, in seditions, in labors, in watchings, in fastings" (2 Cor. 6, 4-5 [Douai]).
In today's world, smothered by pride and sensuality, the concept of fasting stands out as a great, if not repugnant, contradiction. Yet, fasting disciplines the body and brings into line the wayward desires of the flesh, that is, the unruly inclinations of our lower nature. By fasting we unite ourselves to God since we learn by our sacrifices to think of God and unit our small sacrifices with his great sacrifices, not that anything is lacking to the suffering of Christ but that we are called to partake in it. As St. Paul puts it, I "Fill up in my body those things which are wanting to the suffering of Christ in my flesh, for his body, which is the Church" - Col 1:24 Fasting raises our hearts and minds to the contemplation of heavenly things, aiding us to fulfil the universal call to sanctity. Conversely, the glutton is equated with being an enemy of Christ's Cross (Phil. 3, 18).
Some quotes from the Church Fathers :
The Didache (C. 90 - 150 A.D.): "...The teaching of these words is this. Bless those who curse you, and pray for your enemies: fast for those who persecute you...Do not let your fasts be with the hypocrites. They fast on Monday and Thursday; but you will fast on Wednesday and Friday."
Shepherd of Hermas (C. 140 - 150 A.D.): "On the day of the fast, eat only bread and water and, working out the cost of the food you would have consumed, give a corresponding sum to a widow, an orphan, a needy person...Observe these things with your children and all your household; thus you will be happy."
Tertullian, The Demurrer Against the Heretics, Prayer (C. 200 - 206 A.D.): "Likewise, in regard to days of fast, many do not think they should be present at the sacrificial prayers, because their fast would be broken if they were to receive the Body of the Lord...Will not your fast be more solemn if, in addition, you have stood at God's altar?"
St. Ambrose of Milan (+397 A.D.), Ep. 63, 17: "Those who do not believe in the afterlife indulge in food and drink."
St. Jerome (+420 A.D.), Ep. 54, 105: "If you wish to be perfect, it is better to fatten the soul than the body."
St. Leo I, Sermon 13, 1 (Ante 461 A.D.): "The abstinence of him who fasts becomes the nourishment of the poor."