Here are my top 7 Bible verses about casting out demons, sometimes referred to as devils.
Mark 1:34 “And he healed many who were sick with various diseases, and cast out many demons. And he would not permit the demons to speak, because they knew him.”
Interestingly, the first ones to acknowledge that Jesus was God were the demons which is why Jesus didn’t permit them to speak because they often declared “You are the Son of God!” (Luke 4:41) to which Jesus would silence them. By doing so, Jesus shows that He has all authority over the demons including the Devil. Jesus once conquered the Devil’s three-fold temptations during the temptation of Christ in the wilderness (Matt 4:1-11) proving that Jesus has authority over all the demons and even Satan himself. This also shows that the demons, who are fallen angels,  beheld the glory of Jesus Christ before He came to this earth for His earthly ministry and so they knew Him before He entered human flesh and very possibly before there were even humans created.
Luke 10:17 “The seventy-two returned with joy, saying, “Lord, even the demons are subject to us in your name!”
This is what the disciples whom Jesus had sent out said when they returned. He gave them the authority to cast out demons. They didn’t necessarily have that authority of themselves because no human is a match for a demon but when Jesus gives you the authority, then you have His authority.
Acts 19:13-16 “Then some of the itinerant Jewish exorcists undertook to invoke the name of the Lord Jesus over those who had evil spirits, saying, “I adjure you by the Jesus whom Paul proclaims.” Seven sons of a Jewish high priest named Sceva were doing this. But the evil spirit answered them, “Jesus I know, and Paul I recognize, but who are you?” And the man in whom was the evil spirit leaped on them, mastered all of them and overpowered them, so that they fled out of that house naked and wounded.”
I would imagine these itinerant Jews were surprised. They had apparently been seeing or hearing of Jesus casting out demons and maybe some of His disciples had been doing the same thing so they wanted to try it. They got part of it right; they used Jesus’ name but apparently they were not known by Jesus because the possessed man beat them all and they ran out of the house naked and bleeding, showing you don’t really want to fool around with demons if you are not a child of God and thus, don’t have Jesus’ authority.
Luke 8:30, 33 “Jesus then asked him, “What is your name?” And he said, “Legion,” for many demons had entered him. Then the demons came out of the man and entered the pigs, and the herd rushed down the steep bank into the lake and drowned.”
This was not just one demon but a whole legion of demons and a Roman legion during Jesus’ day could have been anywhere from between 3,000 and 6,000 troops. This could not have been done by any single individual. It took God Himself to cast out so many demons because of the tremendous power that they had collectively. This casting out of demons was even more impressive because the man was so possessed by demons that “he was kept under guard and bound with chains and shackles, but he would break the bonds and be driven by the demon into the desert” (Luke 8:29).
Mark 1:39 “And he went throughout all Galilee, preaching in their synagogues and casting out demons.”
Apparently, Jesus didn’t waste much time casting out demons for from the very beginning of His earthly ministry, he was casting out numerous demons in at least twenty different circumstances that we know about in the New Testament. We see this verse as being part of the same ministry; preaching in the synagogues and casting out demons.
Mark 3:13-15 “And he went up on the mountain and called to him those whom he desired, and they came to him. And he appointed twelve (whom he also named apostles) so that they might be with him and he might send them out to preach and have authority to cast out demons.”
This is clear evidence that Jesus gave the disciples the authority to cast out demons meaning that by themselves, they had no such authority. Remember what happened to the Jews who were trying to cast out demons in their own authority? They were beaten badly and ran for their lives. Jesus gives the authority. It is not something that we take up for ourselves as many try to claim.
Luke 4:41 “And demons also came out of many, crying, “You are the Son of God!” But he rebuked them and would not allow them to speak, because they knew that he was the Christ.”
The final verse about casting out demons was again when Jesus was confronted by demons and they already knew Who Jesus was which is why they once “cried out, “What have you to do with us, O Son of God? Have you come here to torment us before the time” (Matt 8:29) showing that they know that they are headed for torment someday as it says in Revelation 20:9 where they will be “thrown into the lake of fire and sulfur where the beast and the false prophet were, and they will be tormented day and night forever and ever.” They didn’t want that to come “before the time” indicating that the Devil  and the demons know their time is coming and they seem to know when that time will be.
We have no fear of demons or the Devil because he has already been defeated by Jesus at the cross “for he who is in you is greater than he who is in the world” (1 John 4:4). Besides, Jesus already had this authority over them long before He went to Calvary and even before He came to be born as a babe in a manger so I would caution anyone that believes he or she has their own authority over the Devil or demons because some of them gave those who tried this “such a beating that they ran out of the house naked and bleeding.”
Related reading: Bible Study on Demons 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.