One of my dogs has, over the past six years, demonstrated an absolute 100% track record in sniffing out whether women are pregnant. He's never given a single false positive, or a false negative. It's not something I've trained, he does it on his own. And to make it even more impressive, at the point when he gave the earliest signal on one woman, we later found out (through the doctor's ultrasound and dates) that it was just three days after conception. As for cancer, they've been known to accurately sniff it out for years now.
The canine nose is an amazing thing. But that's not the entire story, the amount of their brain that they dedicate to processing smell is huge compared to humans. In terms of the percentage of brain dedicated, they use something like 10-30 times more of their brain for smelling than we do. Smell is, quite literally, their primary sense, in the same way that sight is ours. The saying that "Dogs don't smell a cake, they smell each ingredient" is, quite literally, correct. In using dogs for scent detection, the biggest challenge is usually just our ability to isolate the desired scent to present to the dog, doing the rest is easy for the dog.
The real oddity here is not that dogs have good noses... a ton of animals do. Humans are actually the oddity. There seems to be a negative correlation between intelligence and smelling ability, perhaps because having lots of rational thought takes enough brain space that smelling gets pushed aside. Whatever the reason, looking at primates, as you go up in intelligence, smelling ability goes downhill. We shouldn't be so amazed that dogs can do what they do, but saddened that we can't do the same.
