What we really know:
We've always "known" that dogs are descended from wolves, but that's pretty vague. Actually, they are the same species. Dogs and wolves can interbreed. Geneticists consider dogs, Canis Familiaris, to be a subset of the East Asian variety of the globally-present Grey Wolf, Canis Lupis. Oh, there are some appearance differences, and they behave quite a bit differently around humans, but genetically they are the same thing. Okay, some background:
All "higher life form" cells have pretty much the same makeup. A nucleus that has all the cell's DNA, the instruction-set on how to be a good cell for this species of plant or animal, a cell wall that keeps all the good stuff inside, and a whole bunch of odds and ends that do different things as directed by the DNA, RNA, and various enzymes. One particular set of those odds and ends are called Mitochondria.
Mitochondria are self-contained organic power-packs, kinda like batteries. Actually, if you look at them close enough it's clear that eons ago when life was just beginning the mitochondria were actually independent life forms of their own. In fact, they seem to be very similar to some bacteria.
Whether it was a symbiotic relationship that turned sour, or one hungry cell ate a few of those bacteria but then couldn't digest them isn't clear, but the results are plain. The cell puts up with them and feeds them and keeps them safe, and in return the mitochondria help digest nutrients and export high-energy molecules that the cell can transport elsewhere and get important work done with.
The mitochondria also reproduce by splitting whenever they feel like it, just like any cell does. They just live their entire lives inside the larger host cell. And, it's not just some animals or plants. EVERY multi-celled life form, from elephants and sequoias all the way down to the fungi, has them. Basically, anything more advanced than a bacteria or a virus has them.
Why is this important? It's important because of the way sexual reproduction works. Normal cells reproduce by splitting in half. First the DNA helixes uncoil and split, then the cell itself splits in half and each half uses the DNA strand it got to create the missing half of the helix, becoming a complete cell again. Got that? Right. Of course it only works if the split is even enough that both sides get enough of the odds and ends to function as a complete cell. And, that's the whole story, for single celled life forms like bacteria and mitochondria, and even some larger life-forms like lichens, which are really only large colonies of single-celled organisms.
Now, in sexual reproduction, the female who produces the eggs does so by having an otherwise normal cell split as above, but the two half-cells do NOT regenerate the missing DNA. Instead, they each wait around for the missing DNA to be donated by a special "sperm" cell that is basically nothing but a helping of DNA surrounded by a delivery system. Still making sense? Those half-cells we call 'eggs' cannot live long, but if they get the missing DNA delivered in time they are complete cells. If all the DNA matches up right, the fertilized egg starts to split and grow. In nine months, if you're a human, you get a baby. Elephants take about two years. For dogs and wolves, it only takes about two months, maybe a bit longer. I think that rats are something on the order of a few weeks.
The part that matters here is that the mitochondria are all out in the cell body; they have nothing to do with the cell's nucleus or the DNA contained therein. Thus, an egg's mitochondria all come from the mother. The father does not ever contribute anything to the egg except some DNA for the nucleus. And, since the mitochondria used to be independent life forms in their own right, they have their own DNA that tells them how to do all the work of being mitochondria. That fertilized egg's mDNA is identical in every way to the mother's mDNA, since all it did was split in two. Unless there is a mutation in your mDNA, it will be identical to your mother's, your maternal grandmother's, her mother's, and so on all the way back as far as you can test.
In other words, you can track maternal lines through mitochondrial DNA which is donated only by the mother, the same way you can track paternal lines through the "Y" chromosome which is only donated by the father. If the mDNA is different, you aren't one of that lady's descendants, at least not through her maternal line. You might be descended from one of her sons, but not an all-female line of daughters. If it's the same, you are. Pretty simple. Of course the DNA slowly changes or mutates through the years, but even that is helpful because it happens at a fairly standard rate, meaning that you can see how similar two samples are, giving you an idea of how many years separate them.
Okay, now we can get back to our story. A few years ago (my notes say that this was popularly reported in the November 2002 issue of the magazine "Science"), some researchers tracking mitochondrial DNA were able to establish that all dogs are descended from no more than three different East Asian Grey Wolves. All of them. German Shepherds, Mexican Chihuahuas, Australian Dingos, Vietnamese dinner, Scottish Terriers, Japanese Chin. All dogs. Further, various clues that I don't completely understand apparently show that this split from wolves happened about 15 thousand years ago. Three wolves from northern China or Mongolia.
This is backed up by noting that the oldest consistent sets of dog/wolf remains ever found with human remains are from that age, and that part of the world. Note that word 'consistent'. Oh, we find scattered wolf remains buried with people earlier than that, all over the world, from accidental adoptions, but in northern China and Mongolia the finds are far denser, and from there everyone else got dogs, too.
This looks almost like the way military technology spreads. Someone invents the bow and arrow, or the chariot, or the crossbow, or the gun, or the tank, or the nuclear bomb, and before the century is out everybody and their cousin has them. In this case, someone invented a multi-use weapon system we call "the dog". We used that weapon system to hunt, to guard, to herd, to fetch, to provide companionship.
Still, wolves and humans have been in contact as long as there have been wolves and humans. Most of that contact has been violent. Both are hungry, and both eat the same things. If one kills a moose, the other wants to take it from the killer. And, when they get hungry enough, the wolves and humans have no problems eating each other. In many areas, the two are the only candidates for the position of apex predator. The two species try hard to clean the other out of 'their' territory.
There must have been a good reason why everyone suddenly decided that the big bad wolf was really their friend. And, the Mongolian nomads must have had an awfully good reason to put up with these wolves long enough for them to become the obedient and loyal dogs everyone knows and loves today.
Don't say 'docile', though. A week doesn't pass without a news story from somewhere about a mistreated dog proving that it still has a wolf's genes and turns on its tormenter. Or, sadly, in its desperation to control some part of its environment, strikes out at someone helpless who had nothing to do with its mistreatment. Worse, people often try to breed dogs for wolf-like behavior, although that's a waste of time and effort and shows a lack of understanding. The capacity for that behavior is already there. They already ARE wolves. Trying to breed dogs to 'be like' wolves is silly.
It's not true that Pit Bull Terriers are more vicious than other dogs. It is true that, since they have that reputation, people who want vicious dogs tend to start with that breed and mistreat them until they bring out the behavior that any dog would show. When I hear "Look at that vicious Pit Bull" I hear "Look at that mistreated dog". A poodle treated the same would react the same. The only differences between a poodle and a pit bull are size and build. And, some poodles are pretty big.
On a related subject, modern humans spread from Africa all over the world about 50-60 thousand years ago. They even reached a lot of places separated from the "old world" by open ocean. Everywhere except the Americas. And, actually, when you look closely enough, except for most of eastern Siberia. For about 40 thousand years, there were humans south of a particular mountain range in Siberia/Mongolia, but none north of it.
Sometime around 15 thousand years ago, that changed. A bunch of Mongolian nomads got past those mountains, wandered north and east, settled all over Siberia and Kamchatka, crossed the Bering strait, and populated the Americas, becoming our "Indians". The American Indians, often shortened to "AmerInd" to speed conversation, are most closely related to two specific ethnic groups in the old world: The Ainu, those natives of the northernmost Japanese islands, and some small tribes in central Siberia. In fact, the linguists agree that those Siberians speak languages more closely related to some of the Na-Dene group of languages spoken today in Canada than they are to any other Asian languages.
Okay, actually we're mixing up two separate ethnic groups. If we're being honest, it may have been more than two, but one large group of AmerInds that share a common language family are more closely related to the Ainu than they are to the rest of the AmerInds, and another large group of AmerInds that share a common language family are more closely related to those Siberians than they are to the rest of the AmerInds. Thus, at least two separate migrations, right?
.... There is more of this story ...