There are at least three major theories regarding the link between autism and vaccines. I believe that it is generally accepted by the "vaccines as trigger" groups that there is a genetic component or predisposition to develop autism in a susceptible child after an environmental trigger.
1. Autism is caused by exposure to thimerosal. Evidence of Harm is a great book that clearly sums up a lot of the controversy and evidence supporting a link between thimerosal and autism.
2. Another theory is that the MMR shot causes autism. That is pretty controversial because it caused rates of vaccination with the MMR to plummet in
3. Autism is caused by some combination of both thimerosal and the MMR.
The reason this issue has not died is that up to 2/3 of the parents of children with autism believe it was triggered by vaccines. Independent and honest studies have not yet been done. What has generally happened is that some research is thrown together, the media, the CDC, the NIH, et al. announce that yet another study definitively proves there is no link. Parents, doctors, researchers look at the studies and see lack of independence, faulty criteria, etc. and reject the study because of multiple flaws. It convinces no one who was not already convinced; yet, the average person, doctors, professionals, who don't even give it a cursory look, assume it was a well designed and valid study.
I'm going to have to break this down further because I didn't even touch on genetics and that's a huge issue. Nor did I get to which theory I believe triggered it in my kids.