Jesus gave the 12 disciples some pretty special authority when sending them out on missions to the Jewish population. Does this authority apply to us today? The verses where we see the details are:

When Jesus had called the Twelve together, he gave them power and authority to drive out all demons and to cure diseases,
Luke 9:1

Jesus called his twelve disciples to him and gave them authority to drive out impure spirits and to heal every disease and sickness.
Matthew 10:1

He appointed twelve that they might be with him and that he might send them out to preach and to have authority to drive out demons.
Mark 3:14-15

This can (and should) raise various questions in our minds:

Do Christians today have power and authority to drive out all demons and to cure diseases?

Was this only temporary for this particular mission only?

Was it only for the Apostles, or for all Christians permanently?

Our experience is that we don’t generally have this power, and we don’t generally see it in Acts or the epistles.

Paul considered that he had special authority as an Apostle:
I persevered in demonstrating among you the marks of a true apostle, including signs, wonders and miracles.
2 Corinthians 12:12

If these marks showed he was an Apostle, then they must be things that other believers do not do. Hence we should not expect to personally replicate them. This lends support to the idea that this authority that Jesus gave to the 12 was unique to them, plus Paul when he was empowered as an Apostle.

This idea of the authority being limited is supported by what we see in Acts.

Everyone was filled with awe at the many wonders and signs performed by the apostles.
Acts 2:43

The apostles performed many signs and wonders among the people.
Acts 5:12

However, it is true that Acts records one non Apostle doing signs and wonders:

Now Stephen, a man full of God’s grace and power, performed great wonders and signs among the people.
Acts 6:8

Against that idea is the fact that Jesus also gave 72 others authority to heal (Luke 10:1,9) and cast out demons (Luke 10:17). On the other hand, the instructions given to them were fairly unique, and occurred before Jesus’ death. This is important because Jesus changes the rules just after the Last Supper:

Then Jesus asked them, “When I sent you without purse, bag or sandals, did you lack anything?” “Nothing,” they answered. He said to them, “But now if you have a purse, take it, and also a bag; and if you don’t have a sword, sell your cloak and buy one.
Luke 22:35-37

This may mean that some of their authority (or of the 72) also changed after Jesus’ death.

How did the Apostles express their authority when they were using it?

When healing, Peter says “In the name of Jesus Christ of Nazareth, walk.” (Acts 3:6), Paul “called out, “Stand up on your feet!”” (Acts 14:10) and in Malta “Paul went in to see him and, after prayer, placed his hands on him and healed him.”

When casting out an evil spirit, Paul says “In the name of Jesus Christ I command you to come out of her!”

For the other signs, we have no descriptions of how the Apostles acted or what words they used. Peter and Paul were both pretty bold, telling those being healed, and an evil spirit, what to do. But maybe we don’t have that same degree of authority today.

However even Paul’s authority as an Apostle was limited.

Paul couldn’t heal Timothy’s stomach problem (1 Timothy 5:23) nor could he heal Trophimus at Miletus (2 Timothy 4:20) and Epaphroditus “nearly died” in Rome (Philippians 2:25-27).

Paul himself also had his share of problems. It seems that he had problems with his eyes. He notes that he writes with big letters (Gal 6:11) – he normally had someone act as a scribe for him – and in Galatians 4:15 he says “I can testify that, if you could have done so, you would have torn out your eyes and given them to me.” This only makes sense if Paul had eyesight problems that were not healed. In fact, it was because of his being ill in some unpleasant way that he first made contact with the Galatians (Gal 4:13-14).

Given the lack of instruction in the NT that we would expect if these signs were to continue past the Apostolic age, we probably should conclude that widespread use of these signs is now unlikely. However, in 1 Corinthians 12:9, Paul says that some are given gifts of healing, so we should still expect healings to still occur under their ministration.

How are the rest of us to behave? In James 5:14-15, the healing of the sick seems to be a low key corporate activity of the elders.

Now, it is true that Jesus, when referring to his miraculous works, told his disciples that “whoever believes in me… will do even greater things than these” (John 14:12). But what is these greater things? They are available because Jesus is going to the Father (vs 12). What is not then available but will be because of Jesus going to the Father? Jesus has a similar discussion in John 5:20ff. There he also refers to “even greater works”. But in that context, it becomes obvious that he is referring to giving eternal life (vs 21-26) and judgment (vs 27). This is the greater work that Jesus disciples will be able to do – to proclaim that salvation has been won by Jesus’ death on the cross, leading to people being granted eternal life! This is of far greater significance than doing some miracles that have temporary effect.

I previously discussed similar material here.