I'll put in the little that I know, from The Pursuit of Oblivion by Richard Davenport-Hines.

The growth of south American cartels began in the very late 60s/early 70s in response to a crackdown on drug smuggling by the US. In 1969, the Nixon administration launched Operation Intercept aimed at supplies of Marijuana from Mexico, which "result[ed] in a near shutdown of border crossings between Mexico and the United States" (this quote is from wikipedia). This era saw the beginning of The War on Drugs.

There are three notable features here:

1. increased surveillance of borders
2. increased pressure on foreign governments to take action, and support for this action (often military or paramilitary)
3. a move from softer (eg. marijuana) to harder drugs (eg. cocaine).

The first two features meant that drug production and smuggling became a more sophisticated, organised operation. They "drove small, independent Mexican suppliers out of business and thus reserved the market for larger organised trafficking gangs commanding more sophisticated resources." The second factor also increased the incentive to subvert local governments.

The third feature is driven both by supply and demand. Punitive policies for softer drugs pushed people towards harder ones. The risk:reward ratio for harder drugs is generally better (eg. if it's not much harder to smuggle a kilo of cocaine than a kilo of marijuana, go for the one you can make more money on!). However these harder drugs often need more infrastructure - it's pretty easy to grow and prepare marijuana, even in large quantities, but for decent cocaine production you need some chemicals and you probably want a laboratory (so that an 80s action hero can come and blow it up). (It's also worth noting that legitimate companies had already been pushed out of producing drugs like cocaine.) So the change in the drugs being produced also encouraged the growth of larger organisations.