Miocene

The Miocene is the first epoch of the Neogene period and the fourth of the Cainozoic. It started about 23 million years ago and ended about 5.33 million years ago. The rock beds that mark the start and end are well known, but the exact dates of the start and end of the period are uncertain. The Miocene was named by Charles Lyell. The name comes from the Greek words (', “less”) and (', “new”) and means "less recent", because it has 18% fewer modern sea invertebrates than the Pliocene.
The animals at the end of the Miocene are different from those at the start. What happened was climate change. The biota becomes 'modern' because the climate has become more like it is today. That much is certain, but what is not certain is the exact cause of the climate change.
As the Earth cooled, it went from the Oligocene epoch, through the Miocene, and into the Pliocene. The Miocene boundaries are not set at any particular world wide event. They are set at regional boundaries between the warmer Oligocene and the cooler Pliocene epochs.
The plants and animals of the Miocene were not yet modern, and familiar present-day species had not yet evolved. Modern families of mammals and birds existed. Whales, seals, and kelp spread. Modern sharks appeared. Grasslands became more common. Mammalian browsers became less common, and grazer species became more common. About 100 species of ape lived at that time. They lived in Africa, Asia and Europe. Cetaceans were very common in the seas. The gigantic shark "Carcharodon megalodon" may have preyed on them.
The standard reason why the Earth's climate varies is that there are Milankovich cycles. They cause variations in the Earth's orbit. These changes affect the climate. Changes taking place "at present" have to consider the influence of humans as well. Over long periods the position of continents and the growth and decay of mountain ranges can also have big effects.
Climate.
The climate was warm in the Miocene, especially in the first half. 
Then the global climate rivalled that of the Oligocene. The diagram shows that throughout the Oligocene and the first half of the Miocene, climate remained very warm.
Lower temperatures.
The Miocene warm period began 21 million years ago and continued until about 14.5 million years ago. Then global temperatures took a sharp drop — it is called the "Middle Miocene Climate Transition" (MMCT) or "Middle Miocene disruption". 
By eight million years ago, temperatures dropped again, and the Antarctic ice sheet grew. Greenland may have had large glaciers as early as seven or eight million years ago. The climate for the most part remained warm enough to support forests well into the Pliocene.
Impact events.
A large impact event occurred during the Miocene. The date is very uncertain. The event formed the Karakul crater (52 km diameter), in Tajikistan which is estimated to have an age of less than 23 mya or less than 5 mya.
Later Miocene.
The large mountain ranges: the Himalayas, the Andes and the Cascades continued to go upwards. This was due to movements of continental plates grinding against each other. The movement of India into Asia, and the Americas moving against plates to the west caused all these area to buckle up into large ranges.
How would new mountain ranges lower global temperature? This has several possible causes. A falling CO2 would cause the temperature to drop, so the real question is, what would cause the CO2 to drop? One type of cause is CO2 being sequestered (hidden away) by, for instance, organic remains not being recycled. A quite different type of cause points to changes in the Earth's orbit or changes in the heat given out by the Sun (called "insolation").
Africa.
Africa (and elsewhere) was much more forested than today, and the herbivorous mammals were mainly browsers (eating leaves) rather than grazers (eating grass). The advantage was with browsers because Africa was generally forested. 
In the second half of the Miocene temperatures dropped, and grasslands began to expand. After the mid-Miocene climate change there grew vast grasslands in place of the forests which were there before. The browsers had teeth and behaviours which suited forests, and they largely died out. The modern herbivores are almost entirely grazers which "mow the lawns" of the huge African grasslands. This can be seen by comparing their teeth with the teeth of species from the earlier part of the Miocene.
"All flesh is grass" (Hebrew: כָּל־הַבָּשָׂ֣ר חָצִ֔יר kol habbasar chatsir) is a phrase from the Old Testament book of Isaiah, chapter 40, verses 6–8. It applies from the last part of the Miocene to the present day, at any rate so far as land animals are concerned. The steppes of Asia, the mid-West of the USA and the grasslands of Africa all offer the same lesson: that when the temperature and rainfall dropped, most of the forests changed to grassland. Atmospheric carbon dioxide is the other factor which research looks at.
One fundamental cause of the change was the drop in rainfall in Africa and Arabia. This was partly caused by the rise of the Himalayas, which interfered with the flow of air from the wet tropical parts of the East. A major and permanent cooling occurred between 14.8 14.5 mya in the Langhian stage. However, as mentioned above, the grasslands expanded all over the Earth, not just in Africa.
There was a major growth in the Antarctic ice sheet. Ice cores tell us what happened: 18O:16O is a proxy for temperature.
In an indirect way, all this affected human evolution. The reduction in forests led to an expanse of grasslands with some trees. Into this more open area the Australopithecines later ventured out.
Mediterranean.
Another great event, which undoubtedly affected climate, was the refilling of the Mediterranean basin. The so-called Zanclean flood is thought to have refilled the Mediterranean Sea 5.33 million years ago.
This reconnected the Mediterranean Sea to the Atlantic Ocean. It is possible that even before the flood there were partial connections to the Atlantic Ocean.
According to this model, water from the Atlantic Ocean refilled the dried up basin through the modern-day Strait of Gibraltar. The process took up to two years.
The flood may have affected global climate. The much smaller flood triggered when Lake Agassiz drained did result in (or coincide with) a cold period.
Africa and Eurasia.
During the early Miocene, the Arabian Peninsula collided with Eurasia. This cut the link between the Mediterranean and Indian Ocean. It let animals move between Africa and Eurasia, (elephants into Eurasia). In the late Miocene, the connection between the Atlantic and Mediterranean shut. This caused the Mediterranean Sea to almost completely evaporate. The Strait of Gibraltar opened and the Mediterranean refilled at the Miocene-Pliocene boundary: the Zanclean flood.
The Americas.
North and South America continued to drift westward. As they did so, their western edges gradually built up, and their eastern edges trailed.
There was as yet no land connection between the two continents. However, many groups can cross water to some extent. This is illustrated by the mammalian fauna of Madagascar, which is mostly got from Africa even though the two landmasses separated 120 mya.