The simplest and, imo, neatest is the classic straight sided cut. You’ll need to get yourself some edging shears and a straight spade or half moon edger.

Decorative concrete curbing with a “mower edge.” We had this installed in our backyard to make the mowing less onerous. We were able to create curving lines between our lawn and borders where shrubs, trees and flowers are within bark mulch. We simply laid garden hose where we wanted the concrete edging to go, and the company installed it exactly as per our wishes. My husband can now get our backyard done in 20 minutes. He can run the mower wheels along the edging. We opted to have wire strung through the edging so that with frost heaving, the edging doesn’t budge. In 5 years, it hasn’t moved at all. We are very happy with this.

A concrete curb is good but it has to go deep enough that grass roots will not go under. We've used steel landscaping barriers for literally decades.