Answer: The traditional sharp vertical hand cut edge (cut with an edger or sharp flat spade) looks very tidy when well maintained and helps keep grass from encroaching into the beds.
Another method is to use a heavy layer of mulch along the edges of the planting areas to deter plant growth in or out and allow you to mow the lawn right to the edge.
There are commercial edger strips available as well. Lightweight plastic tends to heave in the freeze-thaw cycle, but heavy grade metal and wood strips usually stay in place. Both good quality wooden and metal edger can be custom shaped on site to fit curves. This provides an edge to keep lawn grass out of the beds but may still require weed whacking or edge trimming.
Yet another method is to use a mowing strip along the perimeter, meaning a narrow band of concrete, brick, or similar hard paving material set so that the mower wheel can run on it thus allowing the lawn to be mowed cleanly yet eliminating the need to trim the grass along the edges.
Using straight lines or broad sweeping curves to define planting areas, and consolidating planting areas instead of using many small ones, can also help streamline mowing and edging as well as limit visual clutter in the landscape.
I hope this gives you some ideas.
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