From the detection of gravitational waves generated in space over a billion years ago, to discoveries in genetics here on Earth, we've collected the most compelling science breakthroughs and advances of 2016. Thanks to magnificent, hard-working scientists and researchers around the world, science keeps marching ever forward. And this year saw some discoveries that are absolutely brimming with the promise of greater discoveries, breakthroughs and quality of life in the future.

Sagan discusses the story of the Heike crab and artificial selection of crabs resembling samurai warriors, as an opening into a larger discussion of evolution through natural selection (and the pitfalls of intelligent design). Among the topics are the development of life on the Cosmic Calendar and the Cambrian explosion; the function of DNA in growth; genetic replication, repairs, and mutation; the common biochemistry of terrestrial organisms; the creation of the molecules of life in the Miller-Urey experiment; and speculation on alien life (such as life in Jupiter's clouds). In the Cosmos Update ten years later, Sagan remarks on RNA also controlling chemical reactions and reproducing itself and the different roles of comets (potentially carrying organic molecules or causing the Cretaceous–Paleogene extinction event).

Adam Rutherford meets a new creature created by American scientists, the spider-goat. It is part goat, part spider, and its milk can be used to create artificial spider's web. It is part of a new field of research, synthetic biology, with a radical aim: to break down nature into spare parts so that we can rebuild it however we please. This technology is already being used to make bio-diesel to power cars. Other researchers are looking at how we might, one day, control human emotions by sending 'biological machines' into our brains.

Are the wealthy just born in the right place at the right time? Are the poor victims of a system designed to keep them down? Or do physics and biology determine who is rich and who is poor? Throughout history, distribution of wealth is governed by hidden forces: DNA, environmental stress, patterns of human migration and even the laws of thermodynamics! Nature seems to demand winners and losers in life. But does this mean greed is king, and the rich can take what they want? Or is cooperation – between microorganisms, monkeys, and humans – more essential to survival of a species?

Alice Roberts tries to find out how Stone Age people reached North and South America for the first time. She finds out about an ancient corridor through the Canadian ice sheet that might have allowed the first humans through. Old finds in Chile though point to a whole different route for the first humans making it there.

Our lifespan is increasing by 2.5 years every decade - and a third of all babies born today can expect to live to 100. But living longer can come at a cost. Old age itself brings with it a range of debilitating illnesses, many of which are the result of accumulating damage during our lifetime. Three diseases in particular have become the main killers in the developed world - cancer, heart disease and dementia. But a revolution in bio-medicine is now offering new hope for the treatment of these ailments, and the potential to extend our lives still further. Methods such as gene editing and stem cell therapies are transforming the way medicine can conquer disease today. "How to Live Longer" counts with the guide of the Nobel laureate Sir Paul Nurse, for whom the big question isn't just what science can do to fix our bodies and extend our lives, but whether it's right to use all the tools and techniques available.