Cats are funny. They just are! But what does their body language tell us? Here are some assumptions:
Cats will twitch the tips of their tails when hunting or angry, while larger twitching indicates displeasure. They may also twitch their tails when playing. A tail held high is a sign of happiness, or can be used as a greeting towards humans or other cats (usually close relatives) while half-raised shows less pleasure, and unhappiness is indicated with a tail held low. A scared or surprised cat may puff up its tail and the hair along its back may stand straight up and turn its body sideways to a threat in order to increase its apparent size.
Tailless cats who possess only a small stub of a tail move the stub around as though they possessed a full tail, though it is not nearly as communicative as that of a fully tailed cat. Touching noses is a friendly greeting for cats, while a lowered head is a sign of submission. Some cats will rub their faces along their guardian's cheek or ankles as a friendly greeting or sign of affection. This action is also sometimes a way of "marking their territory," leaving a scent from the scent glands located in the cat's cheek.
Cats also lick both each other and people (e.g. their owners). Cats lick each other to groom each other and to bond together (this grooming is usually done between cats that know each other very well). They will also sometimes lick people for similar reasons, that is, to "groom" them and to show them caring and affection.
When cats are happy, they are known to paw their guardian with a kneading motion. Cats often use this action alongside purring to show contentment and affection for their guardians or other times it can be when the cat is in pain or dying it is said to be a way of comforting itself. It is instinctive to cats, which use it when they are young to stimulate the mother cat's breast to release milk during nursing. As a result, cats hand-raised by humans may lack this reflex.
Pawing is also a way for cats to mark their territory. The scent glands on the underside of their paws release small amounts of scent onto the person or object being pawed, marking it as "theirs" in the same way they would urinate to mark their territory.
Yawning in front of their owner and blinking behavior is common in cats and may be a sign of trust or affection. Cats will respond to a human who dramatically closes and opens their eyes by reciprocating the action. This perhaps illustrates a remarkable aspect of cat intelligence; that they are able to identify and relate part of their own anatomy to the same structure on another species.