Monkeygrass is a name for two similar plants that are popular for borders and groundcover. Also known as lilyturf, both types of Monkeygrass are versatile, being able to handle sun, shade, and different soils. Trouble is, one of them looks great and the other is an aggressive bully (Liriope spicata) that looks to take over. It sends out shoots and spreads far and wide. While you may have tried pulling or tilling, controlling it requires persistence.
Two kinds that look alike
Monkeygrass is the popular name for two look-alike plants that are used for borders and groundcovers. One type, Liriope muscari, is well mannered and stays where you plant it. The other kind, Liriope spicata, is very aggressive and difficult to control.
Use a Broad-Spectrum Control
Monkeygrass is a tough customer, but it can be overcome. You may need to use a control product such as Roundup® Poison Ivy & Tough Brush Killer several times. Just be careful not to spray it on the plants you like, since it's a non-selective herbicide and will harm the plants in comes in contact with. Just be patient: it will work.