This came out in 1966, about nine years before I was born. I'm sure I must have seen it when I was a kid, sometime in the 80s, though I don't remember anything about it beyond the basic premise. Anyway, the novelization of the movie was written by Isaac Asimov, who later (1987) wrote a book called "Fantastic Voyage II: Destination Brain." I'm sure I had at least one of those books, but I don't remember whether I read either one. However, I assumed the movie was based on the first book, but looking at Wikipedia now, it says it wasn't. (It also says a lot of people assumed it was, so at least I'm not alone.) Well, I got the movie on DVD in 2016 (as a double feature with Voyage to the Bottom of the Sea).
So anyway, the United States and an unnamed enemy (presumably the Soviet Union) have both developed the technology to miniaturize anything, including people. However, both sides consider it virtually worthless, since the process reverses itself automatically after just an hour, which doesn't give them enough time to do anything practical. But now one scientist, Dr. Jan Benes, has figured out how to fix that problem. I guess he defects to the U.S. to share the secret with us rather than them. However, while he's being transported from the plane to a secret government facility, the enemy attacks the convoy of cars and motorcycles that was escorting him. Our people manage to get him to safety, but unfortunately, he suffers a brain injury, and an operation must be performed very soon, or he'll die. The problem is that the blood clot can't be reached without killing him... at least by conventional methods.
So, a team is assembled to board a small, specially-designed submarine called the Proteus, which will be miniaturized and injected into Dr. Benes's carotid artery, so that they can travel to the blood clot and remove it with a laser. The pilot of the Proteus is Captain Bill Owens. The navigator is Dr. Michaels (Donald Pleasence). The person who will be performing the laser surgery is Dr. Peter Duval, who is accompanied by his assistant, Cora Peterson (Raquel Welch). The final member of the crew is an agent named Charles Grant. (I think he's in the CIA, or something. And I guess maybe he was the one who got Benes out of Russia or wherever, in the first place, though I wasn't really clear on that.) On the sub, Grant is given the duty of manning the communications, but that's not the real reason he's there. Before the mission begins, Grant is told that Duval is suspected of being a potential assassin, who may try to kill Dr. Benes from the inside. So Grant is there to keep an eye on him. And he's supposed to take orders from Dr. Michaels, who is also aware of this suspicion.
Anyway, the miniaturization process takes awhile. It's done in very careful, deliberate stages. First the sub is shrunk to the size of a toy. Then it's placed in an oversize syringe, which itself is then shrunk down, so that finally the sub is small enough to travel through blood vessels. Unfortunately, soon after being injected into Dr. Benes, they encounter an unexpected current that knocks them off course. So they have to plot a new route to the blood clot, detouring through the heart, lungs, and inner ear, before finally reaching the brain. Along the way, they have to deal with lots of obstacles, and come up with makeshift solutions on the fly. Meanwhile, the Proteus is in frequent communication with the military and a technical support team, who provide some help from the outside.
I don't want to spoil any details of the journey, nor how it all turns out. I will say there is a plot twist that I saw coming all along. And I'll say that there were a lot of plot holes that you just have to ignore. As for the visual effects, I thought some of them were decent and some were just ridiculous. And... some of the dangers the crew faced actually seemed genuinely scary to me, or at least tense. (None of it really looked scary, but the idea of the dangers made me concerned for their safety.) Anyway... I didn't think the movie was particularly good or bad, but it was okay. And it created the Fantastic Voyage Plot trope, which has been used in lots of TV shows and movies and things, some of which I've seen and enjoyed more than this movie. So I give the movie props for that, anyway.