Fish dominate the planet's waters through their astonishing variety of shape and behaviour. The beautiful weedy sea dragon looks like a creature from a fairytale, and the male protects their eggs by carrying them on his tail for months. The sarcastic fringehead, meanwhile, appears to turn its head inside out when it fights. Slow-motion cameras show the flying fish gliding through the air like a flock of birds and capture the world's fastest swimmer, the sailfish, plucking sardines from a shoal at 70 mph. And the tiny Hawaiian goby undertakes one of nature's most daunting journeys, climbing a massive waterfall to find safe pools for breeding.

Mammals' ability to learn new tricks is the key to survival in the knife-edge world of hunters and hunted. In a TV first, a killer whale off the Falklands does something unique: it sneaks into a pool where elephant seal pups learn to swim and snatches them, saving itself the trouble of hunting in the open sea. Slow-motion cameras reveal the star-nosed mole's newly-discovered technique for smelling prey underwater: it exhales then inhales a bubble of air ten times per second. Young ibex soon learn the only way to escape a fox - run up an almost vertical cliff face - and young stoats fight mock battles, learning the skills that make them one of the world's most efficient predators.

There are 200 million insects for each of us. They are the most successful animal group ever. Their key is an armoured covering that takes on almost any shape. Darwin's stag beetle fights in the tree tops with huge curved jaws. The camera flies with millions of monarch butterflies which migrate 2000 miles, navigating by the sun. Super slow motion shows a bombardier beetle firing boiling liquid at enemies through a rotating nozzle. A honey bee army stings a raiding bear into submission. Grass cutter ants march like a Roman army, harvesting grass they cannot actually eat. They cultivate a fungus that breaks the grass down for them. Their giant colony is the closest thing in nature to the complexity of a human city.

Mammals dominate the planet. They do it through having warm blood and by the care they lavish on their young. Weeks of filming in the bitter Antarctic winter reveal how a mother Weddell seal wears her teeth down keeping open a hole in the ice so she can catch fish for her pup. A powered hot air balloon produces stunning images of millions of migrating bats as they converge on fruiting trees in Zambia, and slow-motion cameras reveal how a mother rufous sengi exhausts a chasing lizard. A gyroscopically stabilised camera moves alongside migrating caribou, and a diving team swim among the planet's biggest fight as male humpback whales battle for a female.

Plants' solutions to life's challenges are as ingenious and manipulative as any animal's. Innovative time-lapse photography opens up a parallel world where plants act like fly-paper, or spring-loaded traps, to catch insects. Vines develop suckers and claws to haul themselves into the rainforest canopy. Every peculiar shape proves to have a clever purpose. The dragon's blood tree is like an upturned umbrella to capture mist and shade its roots. The seed of a Bornean tree has wings so aerodynamic they inspired the design of early gliders. The barrel-shaped desert rose is full of water. The heliconia plant even enslaves a humming bird and turns it into an addict for its nectar.

Intelligence and adaptability allow primates to tackle the many challenges of life, and this is what makes our closest relatives so successful. This resourcefulness has enabled primates to conquer an incredible diversity of habitat. Hamadryas baboons live on the open plains of Ethiopia in groups up to 400 strong. Strength in numbers gives them some protection from potential predators. But, should their path cross with other baboon troops, it can lead to all-out battle, as males try to steal females from one another, and even settle old scores. Japanese macaques are the most northerly-dwelling primates and they experience completely different challenges. Some beat the freezing conditions by having access to a thermal spa in the middle of winter. But this privilege is only for those born of the right female bloodline. For western lowland gorillas, it's the male silverback that leads his family group in the rich forests of the Congo basin. He advertises his status to all with a powerful chest-beating display. Most primates are forest dwellers, and one of the strangest is the tarsier – the only purely carnivorous primate. As it hunts for insects the tarsier leaps from tree to tree in the dead of night, using its huge forward-facing eyes to safely judge each jump. Good communication is essential for success in primate society.