Some of the earliest known candles were made in China in 221-226 BC. These candles were made from whale fat. The tapers were made from insect wax and seeds wrapped in paper. Beeswax candles were also used.
Early Japanese candles were made from squirrel wax.
Paintings in Egyptian tombs showed a cone-shaped candle. This form was produced by repeatedly dipping a wick made from either rushes or flax fiber in animal or vegetable fat.
Around the 1st Century, in the areas of modern day Alaska and Oregon, candles were discovered that were made from a fish known as eulachon, "candlefish", which was a type of smelt. When time wasn't readily available to make candles from this fish's oil, the fish were dried out and impaled on a forked stick. Then the fish was lit on fire.
Candles were made from Yak butter.
After the fall of the Roman Empire, olive oil became a scarce commodity. So early Europeans developed tallow candles. Animal fat, the most popular being sheep, was melted in a pot and poured into bronze molds. Wicks were made from the pith (soft spongy center) of rushes. Poor, lower class individual often had to resort to glomming the animal fat onto a stick and lighting it.
The early American colonists possessed few resources readily available for candle-making during their early settlement. So they discovered that bayberries could be used. Since the yield was poor, the use of bayberries didn't last long.
Needless to say, when paraffin was discovered and put into use by the 1830's, everyone was much happier.