There are two Greek words that are used by the biblical writers to convey this concept. Luke always uses some form of pimplemi.
1. What I found interesting was to first look at how it is used in non Holy Spirit contexts.
I have put the filled word in bold, the agent of filling bold and the resulting action italicized.
Luke 4:28 And all the people in the synagogue were filled with rage as they heard these things; 29 and they got up and drove Him out of the city, and led Him to the brow of the hill on which their city had been built, in order to throw Him down the cliff.
Luke 5:26 They were all struck with astonishment and began glorifying God; and they were filled with fear, saying, “We have seen remarkable things today.”
Luke 6:11 But they themselves were filled with rage, and discussed together what they might do to Jesus.
Acts 3:10 and they were taking note of him as being the one who used to sit at the Beautiful Gate of the temple to beg alms, and they were filled with wonder and amazement at what had happened to him.
Acts 5:17 But the high priest rose up, along with all his associates (that is the sect of the Sadducees), and they were filled with jealousy. 18 They laid hands on the apostles and put them in a public jail.
Acts 13:45 But when the Jews saw the crowds, they were filled with jealousy and began contradicting the things spoken by Paul, and were blaspheming.
Acts 19:29 The city was filled with the confusion, and they rushed with one accord into the theater, dragging along Gaius and Aristarchus, Paul’s traveling companions from Macedonia.
Conclusion: When pimplemi is used in non-Holy Spirit contexts it used to describe the influence upon a person of something that affects them internally to act a certain way. The affecting agent in these cases is always an internal emotions produced as a response to some external circumstances.
The affecting agents are rage, fear, confusion, jealousy, or wonder and amazement. The external circumstances that produced these affects were usually hearing the apostles’ or Jesus’ words, or witnessing their miracles.
The effects of rage, confusion, or jealousy resulted in planning or carrying out some kind of violence or arrest. Fear, wonder, or amazement, either resulted in saying something about it or just being in that state.
2. Passages using pimplemi in relationship to the Holy Spirit.
Luke 1:15 “For he will be great in the sight of the Lord; and he will drink no wine or liquor, and he will be filled with the Holy Spirit while yet in his mother’s womb. 16 “And he will turn many of the sons of Israel back to the Lord their God. 17 “It is he who will go as a forerunner before Him in the spirit and power of Elijah, TO TURN THE HEARTS OF THE FATHERS BACK TO THE CHILDREN, and the disobedient to the attitude of the righteous, so as to make ready a people prepared for the Lord.”
Luke 1:41 When Elizabeth heard Mary’s greeting, the baby leaped in her womb; and Elizabeth was filled with the Holy Spirit. 42 And she cried out with a loud voice and said, “Blessed are you among women, and blessed is the fruit of your womb! 43 “And how has it happened to me, that the mother of my Lord would come to me? 44 “For behold, when the sound of your greeting reached my ears, the baby leaped in my womb for joy. 45 “And blessed is she who believed that there would be a fulfillment of what had been spoken to her by the Lord.”
Luke 1:67 And his father Zacharias was filled with the Holy Spirit, and prophesied, saying:
Acts 2:4 And they were all filled with the Holy Spirit and began to speak with other tongues, as the Spirit was giving them utterance.
Acts 4:8 Then Peter, filled with the Holy Spirit, said to them, “Rulers and elders of the people,
Acts 4:31 And when they had prayed, the place where they had gathered together was shaken, and they were all filled with the Holy Spirit and began to speak the word of God with boldness.
Acts 9:17 So Ananias departed and entered the house, and after laying his hands on him said, “Brother Saul, the Lord Jesus, who appeared to you on the road by which you were coming, has sent me so that you may regain your sight and be filled with the Holy Spirit.” 18 And immediately there fell from his eyes something like scales, and he regained his sight, and he got up and was baptized; 19 and he took food and was strengthened. Now for several days he was with the disciples who were at Damascus, 20 and immediately he began to proclaim Jesus in the synagogues, saying, “He is the Son of God.”
Acts 13:9 But Saul, who was also known as Paul, filled with the Holy Spirit, fixed his gaze on him, 10 and said, “You who are full of all deceit and fraud, you son of the devil, you enemy of all righteousness, will you not cease to make crooked the straight ways of the Lord? 11 “Now, behold, the hand of the Lord is upon you, and you will be blind and not see the sun for a time.” And immediately a mist and a darkness fell upon him, and he went about seeking those who would lead him by the hand.
Acts 13:52 And the disciples were continually filled with joy and with the Holy Spirit.
Conclusion: While in the previous passages the internal affecting agent was an emotion that was responding to external circumstances, in these passages the Holy Spirit replaces the emotion as the internal affecting agent and it is not in response to external circumstances. And the Holy Spirit’s filling produces the following effects: leaping of a baby for joy in the womb, a preaching ministry, crying out in a loud voice and speaking prophecy, speaking in tongues, speaking with boldness, possibly the gaining or losing sight, desire to get baptized, and can be accompanied with joy.
3. One passage using a synonym of pimplemi (plerow).
Eph 5:18 And do not get drunk with wine, for that is dissipation, but be filled with the Spirit, 19 speaking to one another in psalms and hymns and spiritual songs, singing and making melody with your heart to the Lord; 20 always giving thanks for all things in the name of our Lord Jesus Christ to God, even the Father; 21 and be subject to one another in the fear of Christ.
Conclusion: It appears here as well that being filled with the Spirit is an internal influence that the Holy Spirit exerts to produce an external result. It usually involves bold speaking. The types of speaking in the examples given are prophecy, speaking in tongues, preaching, exhortations to one another, singing, and giving thanks. It has been accompanied by physical manifestations of gaining or losing sight and well as emotions like joy.
The question is whether this filling of the Spirit continues today. I would say that there is nothing to suggest that the filling of the Spirit does not continue, but some of the effects may have ceased. That gets into a discussion of whether the revelatory gifts like prophecy or tongues continue today. I think it would also be important to explore the connection of the filling with the Spirit to passages that speak of His leading, walking by the Spirit, living by the Spirit, the production of fruit by the Spirit, etc.