There are those who believe pumas and panthers roam the countryside and others who say that without evidence the rumours amount to nothing more than a tall tale.
But there have been 14 reported sightings to Dyfed-Powys Police in the past five years. And numerous claims of seeing big cats in Shropshire, according to figures obtained under the Freedom of Information Act, show that residents across the region have been calling police officers over what they believe is a big cat on the prowl.
From large paw prints in the snow to a lamb mauled by a "panther" and a "puma" in a field, alleged sightings have taken place in Telford, Oswestry, Meifod and Llanidloes.
Big cats have roamed Britain for hundreds of years, according to believers.
Stories of big cats go back to the 1960s and 1970s when it was legal and fashionable to keep exotic animals as pets.
Before the Dangerous Wild Animals Act in 1976, the wealthy could take their lion, tiger or cheetah for a walk without even a licence. But the law was changed to protect the public.
July, Builth Wells, lamb badly injured, lower jaw bitten off. Panther in area.
September, Llanidloes, large black cat sighted in field, size of a golden retriever.
June, Builth Wells, large wild cat chased caller. Not a dog, making growling noises.
August, Brecon, foal eaten by suspected big cat.
September, Oswestry, big cat sighting, running, size of sheep dog.
December, Knighton, sighted large animal, definitely cat, passed vehicle in the dark. Tracks in the snow found two days ago.
December, Knighton, panther sighting in garden. Large cat, jet black in colour.
Large paw prints in snow in the garden, larger than a dog. Possibly large cat.
January, Brecon, six years ago reported big cat footprints. Lots of footprints, quite big, see claw marks.
January, A4067, sighting of large cat type creature. Crouched as if to spring. In headlights looked brown.
February, Brecon, big cat sighted size of large dog. Moved like a cat.
January, Brecon, big cat sighted. Size of a cougar, too big to be any local dog.
March, Brecon, animal footprints found on Black Mountains, may be big cat sighting.
June, Meifod, puma spotted in a field, bigger than a dog.
While many owners gave their pets to zoos or put them down, rumours started that some had released their animals into the wild.
Enthusiasts also think that they were brought to Britain by the Romans and escaped from travelling zoos and menageries for decades.
Over the years each sighting has added a new twist to the mystery of the big cat.
A large black panther-like creature allegedly made a reappearance in Shropshire last March.
Wendy Lochridge was looking out of a window at her home near Oswestry when she saw the creature, but it disappeared into some bushes before she managed to get a photograph of it.
"What I saw was massive. It was over four foot long and it had a long tail," she said. "I watched it. It stood there under a tree before it went in the bushes. It was a good 300 yards away from me.
"It was cat-like but with the long tail. It was definitely a panther. I have cats of my own and it was definitely too big for a normal cat."
"I jumped in my car to see if I could take some snaps but it had long gone."
She added: "I am going to tell some of my neighbours. There are quite a few farms by me and I know that a lot of lambs have gone missing years ago."
In 2008, Shirley Lewis, of Tiphouse Farm near Billingsley, shot four minutes of video of a big cat near her home. The footage appears to show a panther walking through fields, before disappearing behind trees.
Shirley and her husband Steve feared it could be a threat to livestock or even their children. There have been numerous reports of big cats in the Telford area including one in 2008 when Shropshire Star reader Sarah Leeder said she came across one while she was walking on the trail near Apley Woods. And the body of a dead big cat was found on the riverbank on the Severn Way in Shrewsbury in 2009 by paramedic Terry Meagre. However, the British Big Cat Society said despite its size it appeared to be a normal, domestic cat.
A big black cat has also been spotted near Stafford Park, Lightmoor, Broseley and Woodside, as well as stalking along the Silkin Way which runs through the borough.
In November 2006 a big cat sighting by a policeman prompted officers into a late-night search near The White Horse pub in Dawley, Telford. But a search found no trace of it.
Have you seen a big cat in Shropshire or Mid Wales? Email firstname.lastname@example.org or call (01952) 242424.
Jungle giant may be the big daddy:
They've been seen all over Shropshire and Mid Wales. There have been photographic images, shadowy CCTV images, and a whole host of convincing sightings by reliable witnesses which might give you the impression that the countryside is crawling with panthers, pumas, lynxes and other exotic big cats.
But the question still hangs in the air. Where is the absolute proof that they exist? And proof in this case would be the capture of a live "big cat" or the turning up of a body, perhaps through road kill.
However, in February 1989 there was the one and only proven-beyond-doubt case of a big cat in Shropshire.
The body of an Asian jungle cat was found not far from Ludlow and was taken to Ludlow Museum to be identified and examined.
Some believe this big cat had mated with domestic cats, meaning that there could be some monster moggies roaming around, descended from this jungle cat. It was noted at the time that a local domestic cat called Jasper was much larger than normal cat size and had the markings of a jungle cat.
Howard Cheese of the museum was to recall: "It was found dead near Richards Castle. It was bought into the museum and photographs were taken of it, we measured it, and that sort of thing.
"The upshot was that the person who found it paid to have taxidermy carried out on it. It was a jungle cat. I think originally it may have been hit by a car. It had got some form of injury like a broken hip or something like that. We think it had probably died of hunger and that it had been injured and unable to catch anything. It was quite thin when it was found."
"A few years ago they brought in laws where it was illegal to have caged wild animals. Responsible people phoned up zoos and said 'I have a three-quarter grown lion in my back garden, can you fetch it?' The irresponsible ones let them go. There have been quite a lot of sightings, especially around Exmoor. They have got experience of injuries caused by foxes and badgers and the injuries caused by these are of a different type."
The Ludlow big cat, it turns out, was found by a Mr Evans of Richards Castle. It was stuffed and later was being kept in a glass case by Dr Karl Shuker, a zoologist in Halesowen who is, according to his website, internationally recognised as a world expert in cryptozoology – the scientific investigation of mystery animals whose existence or identity has yet to be formally ascertained.
In an interview over 20 years ago, Dr Shuker used the Ludlow big cat as evidence that a new breed of dangerous cat was roaming the West Midlands. He said these cats were the offspring of jungle cats which had escaped from zoos or private collections and had mated with domestic cats.