The five classical animals each correspond to a particular aspect of training, and each embodies a strategy. This document will only attempt to describe the strategies in so far as the author understands them:
Strengthens the bones. Relies on frontal assault, aggression, and power. Lots of breaking, ripping, and tearing. Movements are short and forceful. The tiger fights fiercely, rending, tearing and breaking any open space of skin or limb that is left unguarded.
Trains for muscle strength. More precise than the tiger. Relies on great muscular strength. The Leopard employs many crushing techniques and a lot of internal strikes with the hands. It gets in close to do it's damage.
Trains flexibility. Prefers to work at a distance from the opponent and at angles off-line from his attacks. Requires great flexibility for its attacking and evasion techinques. The Crane has excellent balance and is very at distrubing the balance of others. It has strong wings and uses them often and effectively.
Trains spirit. Uses simple, basic techniques with a challenging strategy of movement complementary to the opponent's (when he advances, I retreat; when he retreats, I advance). Prefers zigzagging motions. The Dragon has a lot of floating motion and a lot of swinging around and whipping.
Trains chi (Internal Energy). The Snake goes for vital points. The eyes and throat being common targets. Snake movements are flowing and rippling with emphasis on the fingers.
The non-classical animals are more concerned with particular strategies and techniques, and not as much with an all-encompassing worldview of combat. Nonetheless, they include some very fine fighitng systems.
Praying mantis style is a very famous style, developed in the 1700s by a fighter named Wang Lang. He supposedly developed it specifically to defeat the monks of the Shaolin Temple. The story is that he had been a very successful fighter who decided to test himself against the monks and failed miserably in his first fight. He then supposedly devoted years of his life to developing a fighting system with which he could defeat them. The result, we are told, is Praying Mantis style (named, it is said, the praying mantis whose defeat of a much larger cicada inspired Wang Lang to study its movements) The monks, in a pattern that was repeated many times in history, adopted the resulting style into the curriculum of the Temple.
Praying Mantis is a combination of a set of sophisticated deflections, counters, and grappling movements with Monkey style footwork (see Monkey style, below). The fundamental strategy of Praying Mantis is to wait patiently for an opening (often in the form of an attack), then tie the opponent's arms with a grappling technique and strike into soft areas and nerve centers.
Shaolin Bird style is one of the older fighting styles, being derived from the very old Lo Han style by way of the later China Hand style that seems to form the basis of much of the familiar Korean and Okinawan styles. (Many of the movements in Okinawan karate and such styles as Tang Soo Do closely resemble movements in China Hand and Shaolin Bird styles).
In Shaolin Bird style the hard, linear strikes and kicks of Lo-Han and China Hand first begin to acquire some of the circularity and fluidity that is characteristic of many later Chinese styles.
The strategic assumption is Shaolin Bird style is that the opponent is larger and stronger. The Bird stylist compensates by leaping in to deliver a flurry of strikes, and then leaping back out of range; or, again, by goading the opponent into a charge and sidestepping while striking. Bird style relies on quick transitions between low and high attacks and stances, sudden reversals of direction, long-range jumps to cover ground quickly, and well-developed stamina. Bird forms emphasize elbows and finger thrusts to soft targets.
Monkey style is an advanced style that demands much of its practitioners. Like Shaolin Bird style, it assumes that the opponent is larger and stronger, and compensates by making it hard to reach or hold onto its practitioner. The Monkey stylist jumps, flips, rolls, and climbs to avoid his attacker. He attacks from peculiar angles, and contorts his body to strike when the opponent believes himself safe.
A monkey stylist, if faced with an opponent who likes the lunging attacks and strong stances of, let us say, a Shotokan stylist, might sidestep the lunge, climb onto the opponent's knee to elbow into the head, and then dive into a roll to escape retaliation. Monkey stylists strike with the backs of the forearms, with the elbows, and with hook kicks and ape kicks (like a front snap, but twisted inward to strike like a roundhouse, but with the leg turned the opposite direction). Monkey stylists like to tease their opponents into rash action and take advantage of their rashness.
Eagle claw style is an animal style derived from the grappling art of Shaolin Chin Na. It relies on very powerful seizing, pinching, twisting, and locking techniques to immobilize or punish an attacker. Eagle claw stylists work hard on developing their grips to facilitate application of painful locks and nerve pinches. Like jujutsu, Eagle claw employs leverage and joint manipulation to defeat an opponent.
There are many more Shaolin animal styles. A suggestive list might include White Ape, Wild Horse, 10,000 Bees, and Golden Centipede. Obviously I have done nothing more here than to suggest the variety of Shaolin animal styles.