Running shoes with a carbon fibre plate in them are here to stay, whether you like it or not (and chances are you do, especially if chasing a PB). A technological advancement in running shoe tech, born out of the Nike Breaking 2 project, now has pretty much every running shoe brand producing carbon plate running shoes – though not all are created equal and they most certainly don't perform the same.
The shoes listed below, unless otherwise stated, are designed for racing longer races from half marathon onwards. That's not to say that they won't feel good on a gentle 5K plod, but it's not what they are ultimately designed for, so the recommendations are based upon use at pace, in longer races.
Why is pace important? When you run fast (whatever fast may be to you), you run with greater efficiency and these shoes are built to enhance that efficiency, so that's when you get the most benefit from them.
Carbon plate running shoes all sit around the 40mm stack height (the max height for a shoe stack as set by World Athletics), which is a lot of foam/shoe. This means that if you're a minimal shoe wearer or just someone who likes to 'feel' the ground when running, these might not be for you, as there is a certain amount of disconnect that takes place with any larger shoe. This is not to say that you'll be stomping around unable to feel your feet on the ground, but there is a degree of instability that comes with a larger shoe.
The shoes have been tested by a variety of runners of all shapes, size and ability over a wide range of distances, but focused primarily on the marathon.