For the mind that is set on the flesh is hostile to God, for it does not submit to God’s law; indeed, it cannot. Those who are in the flesh cannot please God. You, however, are not in the flesh but in the Spirit, if in fact the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him. But if Christ is in you, although the body is dead because of sin, the Spirit is life because of righteousness. If the Spirit of him who raised Jesus from the dead dwells in you, he who raised Christ Jesus from the dead will also give life to your mortal bodies through his Spirit who dwells in you.--(Romans 8:7-10; ESV)
What did the Holy Spirit do when we were saved? What does the Spirit do now? What will He do in the future? The answers to these questions are numerous, but one particular action is brought out in Romans 8:7-11. The simple way to put it is this: "The Spirit gives life to dead people." Paul's reasoning is relatively simple when we boil it down: "Before, we were dead; now, we are not; in the future, we will live even after we die."
Can we be hostile to the omnipotent and holy God and live? The answer is, I believe, no. Indeed, "the body is dead because of sin." There is a very real way in which the unsaved are dead--even while they are "alive." But, when we were saved, the Spirit gave us life.
In the present, we live in and by the Spirit. The Holy Spirit indwells us, empowers us, refreshes us, gives us joy and peace and passion, and sanctifies us. We depend on the Holy Spirit for our soul's very life.
But, in the future, the Spirit will do still more for us. When our mortal bodies have perished, He will give life to our bodies. This is one thing I really don't understand in Romans 8. (I probably don't understand a lot of other things, but even I can tell that I don't fully understand this.) As far back as I can remember, I've been taught that the body is temporal and the soul is eternal. So, I inferred that in Heaven I would not have a body. In fact, it wasn't until recently that I even heard the idea that "in Heaven, we have bodies." So, this passage kind of takes me by surprise every time I read it. I don't quite understand it, but I rejoice at this truth. When our bodies are aching and tired, we can remember that the Spirit will raise our bodies to perfection. When we fear death, we can trust in the fact that God will give our bodies eternal life.
So what does the Holy Spirit do? Among other things, He gives us our very lives.