You will find every kind of monster lurking within these densely-packed 350 pages. There are two headed-babies, mythical mermaids, a giant, detached mouth, not to mention that horrible thing that bursts out of John Hurt's torso in Alien. In a dizzying if not entirely coherent book, Stephen Asma is determined to look unblinkingly at the creatures that lurk on the edges of our consciousness, those sticky slitherers and orange-tusked grunters which hide in wardrobes or in the deep end of the swimming pool, just waiting to pull us down from our well-lit lives into murky mayhem.

Asma starts by calming us down, explaining that a fear of monsters makes perfect developmental sense. Scroll back to pre-history, and it was probably a good idea that we learnt to run from spiders and snakes, tigers, sharks and whatever else fancied having us for breakfast. Aeons later, when westerners first encountered exotic animals such as elephants and hippos it was equally reasonable to read them as monstrous. From here it was a short step for the usually rational Aristotle to accept the existence of a large, hairy quadruped called a Bolinthus that fought its enemies by spraying acid-like excrement great distances. Three centuries later when Pliny the Elder declared that he had seen the corpse of a hippocentaur (half-man, half-horse), most people were still politely giving him the benefit of the doubt.

Where it really gets interesting is when this atavistic fear of the "nondescript", to use the word in its original sense of falling between known categories, fuses with everyday neurosis. That's when you start to get all manner of strange phenomena, such as the witch crazes of the 16th and 17th centuries, when anyone who was feeling tired or anxious jumped to the conclusion that they had been bewitched.

Male anxieties about sexual potency were particularly pervasive, with men rushing to report that their penises had disappeared following a chance encounter with one of Satan's henchmen cunningly disguised as the next door neighbour. One can see the beginnings of a more sophisticated psychology at work here: shrewd commentators suggested that the penises probably hadn't gone missing  it was simply a hallucination, rather than an actual amputation, brought about by a bit of black magic. Here, in a nutshell, was a way of explaining erectile dysfunction in a formula which saved everyone's feelings, apart from the witch's. All you had to do now was hope that "the spell" would be reversed and full potency, in the shape of a penis you could actually see, restored as soon as possible.

Asma is careful not to make his narrative a simple one-way journey between silly gullibility and scientific enlightenment. The arrival of Darwin on the scene, with his talk of descent from monkeys and Nature red in tooth and claw, didn't banish monsters from the public imagination so much as provide new and scarier ways to think about them. Step forward PT Barnum, who obligingly provided all manner of sights and sensations which could, at a pinch, be corralled into a popular version of development theory. One of his most successful exhibits was William Henry Johnson, a black American with a strangely small head. Dressed in a furry body suit, and given a bogus African backstory, Johnson was paraded to a credulous audience as "the Missing Link" between man and monkey.

In this pseudo-scientific atmosphere, anyone who looked a bit odd could be wheeled out for profit. Bearded ladies were no longer God's unfortunates, but grist for clumsy conversations about how gender worked. Chang and Eng Bunker, the original Siamese twins, weren't merely spooky but vaguely educational. General Tom Thumb (Charles Stratton, a midget) wasn't just cute but evidence of what Nature could do when it was feeling fanciful. Emboldened by the way that the American public was becoming more rather than less gullible, Barnum's pièce de resistance was the Fee Jee mermaid, comprised of a monkey's torso sewn on to a big fish's tail. Visiting the mermaid, the man from the Philadelphia Public Ledger caught the public's exhilaration when he trilled how wonderful it felt to be living "in an era of progress".

Asma finishes his tour with an almost obligatory stop-off to consider the way in which we habitually turn individuals and groups we don't like into monsters. It's what Hitler did with the Jews and it's what we are in danger of doing with a whole range of new "threats", from paedophiles to suicide bombers. By assigning people we don't understand to the place on the map marked "here be dragons", suggests Asma, we short-circuit any chance of making things better. Only by letting the monsters who populate our nightmares step into the daylight where they can be seen for what they truly are, will we find a way of living that is hopeful rather than rigid with terror.

Kathryn Hughes's The Short Life and Long Times of Mrs Beeton is published by HarperPerennial.