HEPA (High Efficiency Particulate Air) Vacuum Cleaners filter out most asbestos.
A HEPA filter is made up of hundreds of square feet of filter paper folded into a couple of square feet of space. These filters can remove 99.97 percent of all particles that are 0.3 microns in size or larger. The majority of Libby Amphibole asbestos fibers are between 0.5 and 5 microns in size.
For comparison, one inch contains about 25,000 microns. This means HEPA vacuums, if used correctly, will successfully capture almost all of the fibers of current concern in your home.
Unfortunately, asbestos can be found in a myriad of household materials. Here's what you need to know about asbestos from Thisoldhouse.com.