What is the best kind of vacuum cleaner to use for asthma and allergy issues?

With HEPA filter: A vacuum cleaner with a hepa filter puts out pollen-free, dust-free air from its exhaust end. A vacuum cleaner that blows exhaust upward instead of sideways or backwards has less of a tendence to blow dust from the floor into the air, while one is vacuuming. It's best to wear a mask during vacuuming (available at all drugstores), and to use a room hepa filter afterwards to clear the air.

Hepa: One with either a water filter or hepa filter to reduce dust.