Modern tiles are often geometric and symmetrical or the style has been exaggerated with asymmetrical tiles (different size triangles).
Travertine is a good example of how different shapes can be used to keep the backyard up to date around the pool. The tile comes in many different colours and is able to withstand weather change. The material is also able to absorb water allowing you to walk comfortably without slipping.
Limestone tiles have become common with home improvement and renovations. Not only does the paving tile neaten up the area around the pool but it can also resist different climate changes. Because it has a light appearance, it fits the modern profile.
Modern themes often work for any style house. The modern flair is flexible for most uses whether you have a geometric fountain in the front or a garden full of trees surrounding the pool.
The classic pools have more of a rough layout. Although rough, the area still looks good with its different sized stones and paving tiles. You will often find this look at water resorts for the cave concepts.
Flagstone has a natural appearance with its many shapes and natural colours. The paving tile is slip resistant and can be exposed to any temperatures. For this reason the flagstone tiles can be used for a long period of time.
Slate, which is similar to flagstone, is older and heavier than most tiles. Due to the materials it is composed of, it can be cut into any shape and is very easy to install around the pool. The material also comes in different colours to match the idea you have in mind.
Many classier tiles are made from the same materials as slate and flagstone. This would be the ultimate material to use for the exact picture you have in mind for the older and natural look.