Tiling with natural stone
Tiles and stones that fall under the 'natural materials' heading vary immensely from ceramics in appearance and indeed their application requirements. Identification of the product being installed is essential to allow for the correct preparation and application.
Common issues and queries you can face

Not all natural stones have same characteristics
Natural stones by definition are not regulated in terms of porosity and movement. Sandstone and limestone will be porous, granite and marble will be quite dense, slate could warp.

Difficulty in achieving a flat/level surface
With uncalibrated tiles (i.e. tiles that do not have a constant thickness), such as some slate and terracotta, it is difficult to achieve a flat and level finish on the surface of the tiles. They also require an adhesive that can be used at a bed thickness sufficient to cancel out the variation in the tiles

Adhesives may shadow through light coloured tiles
Some light-coloured limestone/marble tiles are translucent resulting in the adhesive being seen through the tiles. If a grey adhesive is used this can make the tile appear darker in shade once installed. A spot-fixed method of fixing should not be used by tilers as it can result in shadows being seen from the tile face where the adhesive is in contact and also increases the likelihood of point-load breakage.

Tiles may be susceptible to scratching
Grout can scratch soft glazed tiles (such as hand-made tiles) and the surface of soft stone (such as marble).