What you have is a ‘grill pan’

They work well for meat, but the real advantage is that if you have something that gives off a fair bit of liquid, the food doesn’t end up swimming in it.

Mind you, the liquid is still there, and doesn’t drain away, so it’ll still cool off the pan from evaporation, and slightly steam your food, but if it’s pre-heated, you’ll still get decorative grill lines.

My mom used to use it when cooking burgers inside in the winter, or she just didn’t want to be bothered with the outside grill. It’s also useful for cooking vegetables that have been marinated (and left in large slabs).

I have one, but honestly, I tend to put things under the broiler (top heat only in the oven, I know that’s called a grill in other places) for the type of scenarios where you might use this sort of pan.

I would also recommend looking in kitchenware stores for the grill pan scrapers from lodge. (You can get them on Amazon, but they’re often 2 to 3 times the price to cover shipping). There’s also a set that has one of the grill pan scrapers, and one of their regular scraper (which has lots of curves to match multiple pans)

If your alternatives are an oven or non stick pans, these sit perfectly in the middle. They really shine at high temperatures, and with marinated foods.

I personally mainly use mine for meat, as my SO is vegetarian, and doesn't like their vegetables cooked in a meaty pan. However it also works nicely for bread products. I toast my burger buns in it before making burgers, my flatbreads when making kebabs, wraps, naans, all these get a nice toast with grillmarks when I use them. It adds a nice partial char to the food that you can't get another way without burning larger parts of your bread.

You can use it with vegetables as a low-fat solution to frying, or use it to make nice smokey gravies.

However where it really sings is indeed with meat. It can go up to soaring high temperatures, where non-stick pans tap out long before. This is ideal for cooking steak in particular, but also smash burgers (they are thin and need the outside cooked fast if you want any kind of darkening). It is also ideal for cooking anything marinated. If you use a pan or broiler, it could char and burn large parts of your marinade, especially if you use herbs. With this grill pan, it will only burn (char) the lines, and steam in between leaving the dynamic of your marinade intact.

The only downside I have found for this kind of pan is the maintenance. It should be kept well seasoned like all cast iron pans and woks. After cooking, clean it by adding one or two pints of water and a teaspoon of salt, and simmer for 15 minutes to an hour. This will dissolve the non-oil particles and leave the non stick seasoning intact as opposed to using soap. Then dump out the water and wipe the pan with paper towels. (Note: I have found that different foods need different simmer times. Breads need next to no cleaning, and fatty means tend to clean up quite quickly. Leaner meats like chicken etc. tend to get charred more and stick to the pan, and will need longer simmer times - yes, up to an hour - to loosen up, even in a well seasoned pan.) It also gives off large amounts of smoke and steam for an inside pan, and you will need to have your extraction fan on high and preferably a window open as well.

I've had one of these for years, but usually can't be bothered to dig it out.

The only real gain I can see is … it makes nice stripes.

I've seen people claim it's for "lower fat" cooking, but I think that's… ermm … tosh.

Panini press

You can make grilled sandwiches, panini style.

While a real panini press cooks with two hot sides simultaneously, you can come close to that effect by flipping your sandwich while using a heavy lid or foil-wrapped brick to maintain pressure. Or purchase a grill press, preheated to help cook the sandwich.

You can use it for most foods you can grill on a barbecue, like sliced or whole vegetables and fish on (or in) the skin.

Oil the food and have your pan hot before you add the food.

Or what my mother did with hers, she kept it clean, heat it on cold nights, put in the bed before bedtime and take out before tucking the grandkid in.
This does have risks, if too hot the bed can burn.