Before/During the War
Manticores were notably feared creatures that lived within places like Everfree Forest. One was encountered by the Mane 6 during their journey through Everfree to the old castle ruins. The group attacked the enraged manticore, Fluttershy was able to sense that something was off and cut the fight short. She removed a thorn stuck in the manticore's paw and the group moved on.
After the War
Manticores are very dangerous creatures, often preying on weaker creatures such as ponies. One lone hunter killed Clarinet, Monterey Jack's wife. Littlepip's path was blocked in Manehattan by a large group of Manticores, forcing her and the rest of her companions to find an alternate route forward. Another manticore was found in Manehattan, controlled by a ghoul scientist. Another manticore was encountered in Everfree forest, having been consumed by the Black Fungus.
Manticores in other Stories
Brass from Project Horizons, who was a pony-manticore crossbreed capable of controlling manticores around her to do her bidding. She treated them much like one would treat a kitten or cat and called one of the meanest one's in her group a big softie.
A Manticore was hunting Henrietta when she was first introduced in Pink Eyes. This manticore was killed when it bit into Puppysmiles suit, piercing it and releasing the pink cloud within which killed it and caused its body to fuse with a nearby wall.
A manticore has the body and head of a lion, large bat-like wings and a Scorpion tail in place of a regular Lions tail. Two large fangs jut up from the bottom of their mouths. Radiation and Taint has no effect on Manticores so they were able to survive the war unharmed.
Manticores have been shown congreating in large groups and as lone hunters and predators throughout Fallout Equestria & it's various side-stories. Many of them still live within Everfree as shown by a Manticore that was eaten by a black fungus-like plant in Everfree Forest.