Famed astrophysicist Neil deGrasse Tyson takes a tour of the Solar System and the known universe establishing the components of Earth's "address" within the Virgo Supercluster. He then shares the story of the person who championed an expansive understanding of Earth's place in the universe by presenting Renaissance Italian Giordano Bruno's vision of the universe as a limitless expanse of space and time. He then makes an exploration into the Cosmic Calendar, which dates back to the dawn of the Big Bang (similar to the presentation from episode 1 of the original series). The episode ends with deGrasse Tyson narrating how he met his mentor Carl Sagan, who hosted the first Cosmos series.

Rembrandt's success in his early years was as a portrait painter to the rich denizens of Amsterdam at a time when the city was being transformed from a small nondescript port into the economic capital of the world. His historical and religious paintings also gave him wide acclaim. Despite being known as a portrait painter Rembrandt used his talent to push the boundaries of painting. This direction made him unpopular in the later years of his career as he shifted from being the talk of the town to becoming adrift in the Amsterdam art scene and criticised by his peers.

This episode covers the nature of how life may have developed on Earth and the possibility of life on other planets. Tyson begins by explaining how the human development of writing systems enabled the transfer of information through generations, describing how Princess Enheduanna ca. 2280 BCE would be one of the first to sign her name to her works, and how Gilgamesh collected stories, including that of Utnapishtim documenting a great flood comparable to the story of Noah's Ark. Tyson explains how DNA similarly records information to propagate life, and postulates theories of how DNA originated on Earth, including evolution from a shallow tide pool, or from the ejecta of meteor collisions from other planets. In the latter case, Tyson explains how comparing the composition of the Nakhla meteorite in 1911 to results collected by the Viking program demonstrated that material from Mars could transit to Earth, and the ability of some microbes to survive the harsh conditions of space. With the motions of solar systems through the galaxy over billions of years, life could conceivably propagate from planet to planet in the same manner. Tyson then moves on to consider if life on other planets could exist. He explains how Project Diana performed in the 1960s showed that radio waves are able to travel in space, and that all of humanity's broadcast signals continue to radiate into space from our planet. Tyson notes that projects have since looked for similar signals potentially emanating from other solar systems. Tyson then explains that the development and lifespan of extraterrestrial civilizations must be considered for such detection to be realized. He notes that civilizations can be wiped out by cosmic events like supernovae, natural disasters such as the Toba disaster, or even self-destruct through war or other means, making probability estimates difficult. Tyson describes how elliptical galaxies, in which some of the oldest red dwarf stars exist, would offer the best chance of finding established civilizations. Tyson concludes that human intelligence properly applied should allow our species to avoid such disasters and enable us to migrate beyond the Earth before the Sun's eventual transformation into a red giant.

The Arctic and Antarctic experience the most extreme seasons on Earth. Time-lapse cameras watch a colony of emperor penguins, transforming them into a single organism. The film reveals new science about the dynamics of emperor penguin behaviour. In the north, unique aerial images show a polar bear swimming more than 100km. Diving for up to two minutes at a time. The exhausted polar bear later attacks a herd of walrus in a true clash of the Titans.

In 1985, two adventurous young mountaineers, Joe Simpson and Simon Yates, set off to climb the treacherous west face of the Siula Grande in the Peruvian Andes. They were experienced climbers, and climbed "Alpine-style," climbing the mountain in "one great push," without setting up ropes or base camps ahead of time. After dealing with a snowstorm and some dangerous climbing over powder formations, they reached the summit (about 21,000 feet) on the third day. The climb down proved to be far more difficult. Simpson fell and broke his leg badly. Yates decided to try to lower Simpson down the mountain, one 300-foot section of rope at a time. The climbers had run out of gas to melt snow, so they couldn't risk stopping as night came, and a violent snowstorm began. Their plodding, painful journey hit a snag when Yates inadvertently lowered Simpson over the edge of a cliff. In the storm, the men couldn't hear each other's cries, and, Yates, uncertain as to Simpson's position, and gradually sliding down the slope himself, decided to cut the rope that connected them, sending Simpson plummeting to certain death. Miraculously, Simpson survived the fall, and was faced with the prospect of getting off the mountain alone with no food, no water, and a broken leg. In Touching the Void, filmmaker Kevin Macdonald (One Day in September) tells their story, based on Simpson's book, using contemporary interviews with the two men, and a reenactment of their climb and descent, featuring Brendan Mackey as Simpson and Nicholas Aaron as Yates

We move around in space, but we are stuck in a prison of time moving ever forwards. Einstein said, 'The distinction between past, present and future is only a stubbornly persistent illusion.' Is our experience of the ticking clock merely a trick of the mind? Could science ever make the clock move backwards? Experiments in quantum physics are showing that the future influences the present: what happens later limits the choices we think we have now. The laws of physics say visiting or talking to ourselves in the past is possible – but changing history once we get there is not.