"The weapons we fight with are not the weapons of the world. On the contrary, they have divine power to demolish strongholds. We demolish arguments and every pretension that sets itself up against the knowledge of God, and we take captive every thought and make it obedient to Christ." (2 Corinthians 10:4-5 NIV)
While we would greatly overestimate Satan's power by supposing that he can interact directly with us in a physical sense, an equal and opposite error would be to suppose that he does not have access to our minds.
First, while Satan cannot read our minds, he can influence our thoughts. Thus, the Bible instructs us to "put on the full armor of God so that you can take your stand against the devil's schemes" (Eph. 6:11 NIV). Without it, you are a guaranteed casualty in the invisible war; with it, you are invincible. Spiritual warfare is waged against invisible beings that personify the extremities of evil; and their weapons are spiritual, not physical. While they cannot bite us physically, violate us sexually, or cause us to levitate, they can tempt us to cheat, steal, and lie.
Furthermore, it is crucial to note that if we open the door to Satan by failing to put on the full armor of God, he does, as it were, sit on our shoulders and whisper into our ears. The whisper cannot be discerned with the physical ear; it can, however, penetrate "the ear" of the mind. We cannot explain how such communication takes place any more than we can explain how our immaterial minds can cause the physical synapses of the brain to fire; but that such mind-to-mind communication takes place is indisputable. If it were not so, the Devil could not have tempted Judas to betray his Master, seduced Ananias and Sapphira to deceive Peter, or incited David to take a census.
Finally, while fallen angels are not material beings and thus cannot interact with us directly in the physical sense, they are as real as the very flesh on our bones. No doubt much to the Devil's delight we often depict him as either a cartoonish clown with an elongated tail, red tights, and a pitchfork — or as a cultural caricature. Far from silly or stupid, however, Satan appears as a cosmopolitan angel of enlightenment. He knows full well that without our spiritual armor we are but pawns in a devil's game.
In the final analysis, the whole of Scripture informs us that spiritual warfare is the battle for the mind.
For further study, see Hank Hanegraaff, The Covering: God's Plan to Protect You from Evil (Nashville: W Publishing, 2002).
Adapted from Hank Hanegraaff, The Bible Answer Book (Nashville: J. Countryman, 2004).