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HOMO SAPIENS likes to categorise. Putting things in boxes helps us understand the complexities of the world around us – until it doesn’t.

Take the apparently simple organising principle of a species. You might have learned at school that a species is a group of individuals that can breed to produce fertile offspring. But this is just one of at least 34 competing definitions by researchers working in different fields. Ecologists tend to categorise based on lifestyle. Palaeontologists focus on form. Geneticists sequence genomes and then create family trees based on shared, genetically encoded characteristics.

The problem is that evolution – the origin of species – is intrinsically about gradual, random change (see “Think you understand how evolution works? You’re probably wrong”). Charles Darwin recognised that organisms live in populations that can diverge and evolve in different directions, especially if they face different environmental challenges. At some point, they become so distinct that we classify them as separate species. It just isn’t easy to pin down exactly when.

We could just accept that “species” is a fluid, imperfect concept that helps us understand and conserve the diversity of the natural world. Unfortunately, it doesn’t always. This year, for example, genetic analysis of the world’s largest amphibian, the critically endangered Chinese giant salamander, revealed it was actually three species, not one, each requiring different conservation interventions.

Traditional species concepts are further undermined by high levels of hybridisation in nature. One prominent example is the critically endangered red wolf found in the south-east US, which is now thought to be a cross between a coyote and a grey wolf.

Our species isn’t immune to these confusions. In recent years, we have discovered that our ancestors interbred with other hominins, including Neanderthals, Denisovans and a mysterious “species X”. Does this make us hybrids, or does it mean those hominins weren’t separate species, but simply different versions of us?

There probably isn’t a clear answer to such questions. In the end, the whole idea of fixed species appeals to ideas of immutability in nature that now seem rather outdated. Biology is messy, and doesn’t bend to our desire for clean classifications.

Cutting-edge science throws up all sorts of controversial, nebulous and mind-bending concepts. Here’s your guide to how to think about some of the fiddliest of them:

• In the quantum world, uncertainty reigns – or is it all in the mind?
• Think you understand how evolution works? You’re probably wrong
• Why information could be our route to the universe’s deepest secrets
• Who do you think you are? Why your sense of self is an illusion
• Big bang retold: The weird twists in the story of the universe’s birth
• Firms and governments use the internet to spy on us. Should we care?
• D’oh! Why human beings aren’t as intelligent as we think
• Extinction is a fact of life. Could we stop it – or even reverse it?
• No more goody two shoes: Why true altruism can’t exist
• Alien life could be weirder than our Earthling brains can ever imagine
• Why it’s time to call time on the ‘nature vs nurture’ debate
• Dark energy: Understanding the mystery force that rules the universe