Ancient History
The ancient Roman's called their engagement ring the betrothal (Truth) ring. The Romans were the first to wear the ring on the third finger of the left hand.
This surviving tradition seems to stem from the Egyptian belief that the vein from this finger leads straight to the heart. It's thought that the Romans were the first to start inscribing or engraving their rings.

The Middle Ages
The Middle Ages and the Gimmal or "bond" ring was invented, but it's doubtful that this was an engagement ring design. However, sapphires, emeralds and rubies would have been the norm for those who could afford them.
Because diamond is the hardest and strongest mineral on earth it was seen to resist fire and steel and thus symbolize the unbending union of a man and woman in wedlock. So it became more commonplace for the European super wealthy and royalty to give a diamond engagement ring at this time.
Less wealthy citizens would have given a Fede (faith) ring in the form of two clasped hands more akin to the more modern claddagh (clasped hands) engagement rings.

The 18th Century
Diamonds became more readily available when diamonds were discovered in Brazil. Diamond cluster engagement rings were fashionable among the wealthy.

The 19th Century
In South Africa 1870, the vast, newly discovered Kimberley diamond region began to flood the market with not so rare a gem after all! The supply increased whilst the prices fell.
Within 10 years the now famous De Beers Consolidated Mines Ltd. was formed by the Englishman Cecil John Rhodes to control the sale of diamonds throughout the world. Even today they control 65% of the world's diamond trade.
At this time during the history of the engagement ring, the diamond rush gave rise to the notion that the various birthstones were seen to be a rarity (and more desirable) compared to the diamond.
Elaborate engagement rings of sapphire, emerald and rubies (and other precious gems) with diamond accents were therefore more commonplace among those with appropriate wealth.

The 20th Century
From 1880 De Beers were able to control the supply (and price) of diamonds but how were they going to control demand during a period when sales began dropping dramatically (up to 50%) in the 20s and 30s onwards through the great depression?
Just as platinum started to become popular in diamond engagement rings, diamonds were becoming less valued. Platinum was banned for all but war use during WWII and so the platinum diamond engagement rings as we know them today almost died out.
The answer to the problem was a new marketing campaign commissioned by De Beers that began in 1947. Perhaps you've heard the slogan "A Diamond is forever"? This was to mark the beginning of a change in the history of the engagement ring.
Subsequent campaigns would convince families to hold on to their diamonds as family heirlooms... and it worked! Used diamonds were not being released back into the industry which in turn created the demand that De Beers were seeking.
Jewelers were unofficially educated by De Beers to instruct men that two to three months personal wages were an ideal price to pay for the diamond engagement ring that their prospective fiancée's would gladly accept.

The 21st Century
The history of the engagement ring has moved on and demand for diamonds and platinum diamond engagement rings is still rising. The tradition is here to stay. Estimated 78% of all engagement rings sold every year are diamond.