There are some dangers in using wire grill brushes.
How can a grill be safely cleaned without the risk of wires getting into food?
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The grilling industry would be trilled to sell you any number of alternate cleaning devices. These come in three main types.
First, there's the non-wire brushes. The best of these, and what I use, are nylon with abrasive grit. In addition to being non-wire, they're also great for use with more delicate grill types, like my cast aluminum grates. They need to be used while the grill is cold.
Second, you can get grill "scrubbies", which basically attach a heavy-duty kitchen scrubber to a handle. While some of these are wire or metal, since it's in loops it doesn't carry the same dangers as regular wire brushes. These are great for getting off really baked-on messes, but aren't so good for getting between the grate slats.
The third type are scrapers. The most dramatic of these are the wooden scrapers which you first use on a very hot grill to burn the shape of your grill grate into them. I don't know how well these actually work, but they look cool.