DON'T CONFUSE THIS WITH THE STUPID DRUG/TERRORST CONNECTION TV COMMERCIALS

To sum it up: there is now a ton hard proof of the crime family- terrorist connection.
A slew of honest research that I have shamelessly plagiarized include
Harvard University
Senate Hearings
St Andrews College UK
Jane's
Many reliable institutions and groups are connecting the dots linking criminal syndicates with terror networks. Money is the grease that makes these wheels turn. Drug money can finance terror, terrorist learn from the crime families how to launder money, steal large items like planes and trucks, and how to highjack commercial vehicles. The crime families then actually become political actually taking over countries.

The intelligentsia actually doing work in this area have broken it down into seven categories that are divided into four crime-terror relationships. They are
1. actual alliances;
2. what they call "convergence";
3. operational motivations, and lastly;
4. "The Black Hole Syndrome" which goes a long way to explaining this stuff.
As Jane's explains it

Alliances exist at both ends of the continuum, with criminal groups forming alliances with terrorist organizations, and terrorist groups seeking alliances with criminal organizations. Alliances can include one-off, short-term and long-term agreements, and are usually used to gain expert knowledge like, money-laundering, counterfeiting or bomb-making. There is also "operational support" like access to smuggling routes.
The most common alliances exist in the field of international smuggling operations, evident in the cocaine for arms ties developed between the Revolutionary Armed Forces of Colombia (Fuerzas Armadas Revolucionarias de Colombia - FARC), Mexican drug trafficking groups, and Russian criminal groups.

The Harvard study takes it further:

First, it refers to traditional criminal organizations–such as the Russian mafia and Albanian criminal groups– that initially used terror tactics as an operational tool, normally to eliminate competitors, but subsequently to seek political objectives. Second, the fulcrum of the crime-terror nexus refers to terrorist groups–such as Abu Sayyaf and the Revolutionary Armed Forces of Colombia–who initially used criminal activities as a source of financing, but subsequently changed the focus of their ideological beliefs from political to financial. Finally, it may be applied to contemporary civil wars–wars in which factions have evolved from basing their motivations on religion and ideology to crime (for example, the "diamond' wars of Sierra Leone and Angola) In Afghanistan and Central Asia the entire crime-terror continuum is represented. Thus, in addition to providing a base for organized criminal (drug mafias) and terrorist groups (Al-Qaeda), this region is also home to groups that simultaneously appear to be criminal AND terrorist in nature (the Islamic Movement of Uzbekistan).

The end of the cold war drove many criminal and terrorist groups to shift focus. Criminal groups are increasingly engaged in political activity

...in an effort to manipulate operational conditions present in the rising numbers of weak states; terrorist groups have increasingly focused on criminal activities to replace lost financial support from state sponsors. Iraq and Afghanistan for example.

There is motivational convergence in that some criminal and terrorist groups have evolved beyond using terrorism and crime as separate tactics. These groups perform both terrorism and organized crime simultaneously. Furthermore, these hybrid groups have the potential to transform into an entity situated at the opposite end of the crime-terror nexus from which it began.

In its most basic form, the convergence thesis includes two independent, yet related, components. First, it incorporates criminal groups that display political motivations; and second, it refers to terrorist groups who are equally interested in criminal profits, but ultimately begin to use their political rhetoric as a facade for perpetrating solely criminal activities. Meaning that terrorist groups BECOME criminal organizations pretending to be terrorist orgs.

Now the Black Hole part and this is critical; from Jane's again

The final point of convergence noted in the diagram is the 'Black Hole'. It is at this point that the convergence between criminal and political motivations within a single group allows it to subsequently gain economic AND political control over a state. The 'black hole' can contribute to the production of a failed state - such as Afghanistan, Sierra Leone, Somalia and Liberia (get that one), which are states that lack central authority, and displays the characteristics of anarchy;, or they can produce criminal states like North Korea, Myanmar, and potentially the Northwest Frontier Province of Pakistan.

If you are interested further I suggest you go to the Harvard site which MAY have been the source for most others including the world famous Jane's.