Ivy makes an excellent ground cover, but it can grow in so many conditions that it's often considered invasive. It's not a plant you want growing in or near your flower beds because it can choke out the desirable plants until all that's left is the ivy. Species such as English ivy (Hedera helix) and Irish ivy (Hedera helix hibernica) thrive in U.S. Department of Agriculture plant hardiness zones 5 through 11, and they usually require a bit of manual labor to remove.
Pull the ivy by hand. Wear long sleeves, long pants, closed-toe shoes and heavy gloves; the sap sometimes causes skin irritation. Get your kids involved as well. Ivy typically has shallow roots, making it relatively easy to pull out of the ground. Start at one end of the ivy mat and pull backward, removing the vines and roots from the ground. After your children help you make a pile with the vines, ask them to step back to a safe distance while you chop the pile into 1-foot pieces with loppers. Cut any roots visible in the soil where the ivy was, as well.
Cover the ivy with 8 inches of mulch, which can be a combination of a bottom layer of newspaper and mulch such as shredded bark, or simply a thick layer of mulch. This works best when the ivy is contained to certain areas of your flower bed rather than weaving between existing plants you want to keep. For example, if ivy has just begun creeping into your flower bed and is only found around the edges, mulch is an ideal solution to smother it and kill it.
Don protective clothing, including eye protection, and spray the unwanted plants with an ivy-specific herbicide while your kids aren't around. Typical herbicides can't penetrate the waxy leaves of ivy; they just roll off and can drip onto desirable plants you don't want to kill. Spray close to the ivy leaves to contain the herbicide, and follow all manufacturer directions.