In Greek Mythology
They are depicted as being a mix between goats and men. They were the companions of Pan and Dionysos, and known for drinking wine, chasing Nymphs and general drunken chaos, beastliness and mischief.
In the God of War series
Throughout the God of War games, Satyrs have stood as the most formidable opponents in each iteration, able to go toe-to-toe with Kratos and make short work of him if the player is not careful.
In God of War
Satyrs are very talented warriors and are armed with a double bladed staff which can be broken down when needed into two separate sword-like axes. Kratos also encounters a type called a Hades Satyr during his journey through the Underworld.
Kratos encounters these monsters as he fights his way through the depths of Hades. They resemble the standard Satyr, except they're wreathed in hellish flames. They also have the same strength, weapon, and fighting styles as the standard Satyr.
In God of War II
Another type of Satyr, called Satyr Champions, is encountered in God of War II. Armed with two axe-like swords, these Champions are a more violent, much more experienced, and most dangerous version of the Satyr. Satyr Champions are incredibly dangerous and use a variety of acrobatic and agile moves with their axes to attack Kratos. They also have the ability to put their dual axes together into the single double-bladed staff, and then use that as their weapon. By pressing the circle button while close to the Satyr Champion, Kratos will push their weapons down and stab them, then send them flying with a punch, similar to a basic Satyr. When close to death, grabbing a Satyr Champion will make Kratos stab the Satyr with one blade, swing it away with the chains, and then pull it back to a fatal chest stab with the other blade.
In God of War: Chains of Olympus
Satyrs also appear in God of War: Chains of Olympus. They look slightly different than the Satyrs in the previous God of War games, being a little smaller and more goat-like. Kratos mostly encounters them around the Temple of Helios. As weapons, they wield two sai, and attack with fast leaping strikes. Kratos can damage them by grabbing them, and then throwing them over his shoulder. After doing enough damage to them, he can grab them from behind, and cut their throat to kill them. A more powerful version called the Dark Satyr is also found in the Underworld.
They resemble the standard Satyrs encountered earlier in the game, except they have black skin and a skullish head. Kratos encounters them in the Underworld, within the Temple of Persephone. They also fight the same way as the standard Satyrs, except they are stronger and more agressive. After doing enough damage, Kratos can kill them the same way as the standard Satyr as well.
Satyr Grenadiers are like the standard Satyr, except they carry a flask full of explosive material. They attack Kratos by keeping their distance and lobbing their explosive flasks at him. The Satyrs are also extremely hardy in releance to the amount of damage they can take from Kratos himself. Kratos can damage and kill Satyr Grenadiers the same way he does for the standard Satyrs. These guys are mainly encountered in and around the Temple of Helios. There's also a stronger version n the Underworld called a Dark Satyr Grenadier.
Dark Satyr Grenadier
Dark Grenadiers appear similar to the Satyr Grenadiers encountered earlier in the game, except that they have blackened skin, and a skullish head. Kratos encounters these foes in the Underworld, within the Temple of Persephone. Their attack styles are like the standard Satyr Grenadier, except they're even more agressive and stronger. After doing enough damage to them, Kratos can kill them the same way he kills a standard Satyr.
In God of War III
Kratos confronts Satyrs yet again in God of War III. They appear similar to the Satyrs of God of War and God of War II, but are much more challenging enemies. They are very acrobatic, flipping and spinning all around Kratos. They also have very similar attack methods, so similar strategies must be used to defeat them. Most of their attacks can be blocked, except for their hook attack, which they perform after a wall jump. Instead of a hook attack, they can also use a slash attack after wall jumping, which again can be blocked. Once again, Kratos can deliver damage to these goat-headed fiends before they are weak enough to be killed by fighting over the Satyr's staff, and delivering a wicked headbutt to the beast. Once they are close enough to death, Kratos can pull the staff from their hands, slash their face with the hooked end, and javelin the staff through the Satyr's body, pinning it to the nearest wall.