Historically leather was the most common materials used for shoe
soles. Present day shoe soles made of rubber, TPR, PVC, PU or EVA
are the most common. Why?, because rubber lasts longer than leather,
can be formed into grips and is waterproof.
There is various types of rubber however, Crepe rubber for example
is soft and works well as a shock absorber for running shoes. Therefore
most cobblers will have a selection of leather or rubber soles to
pick from. There are also professional cobblers online who will
resole shoes for top branded trainers like Nike. They have exact
replicas, or use replacement soles from the manufacturers.