There are two general categories of pipes: Hand Made ( consists of Freehand shapes made to better represent or "follow" the grain of the wood, and the classically shaped pipes which are mostly turned or machined pieces that have been well established for many years.

Today, most pipes are made of briar, which is a root that is mostly found along the Mediterranean.  Mainly:  Italy, Algeria, Morocco, Corsica, Greece.

Here are examples of "Plateau" cut briar

The cut briar is then lightly sanded to see the grain texture within it

Choosing a shape that will showcase or highlight the grain texture within the briar

The excess briar is then cut off.  This helps shape the pipe and decreases the time of each sanding stage

Before and after stages of the boring of the pipe bowl or "chamber"

The sanding stages are what give the briar a more definitive shape and appearance of a pipe 

The pipe shank is then bored to create a tenon chamber

The draught hole is drilled, by hand, using a very long drill bit

While sanding the pipe, the wood is wet to see the progression of the shape with respect to the grain texture

The chosen mouthpiece is then turned and shaped using a lathe and fit onto the pipe

Sanding the pipe and mouthpiece ( 4 stages)

Finishing touches before staining the pipe