Advantages:

Wood will lower the water’s pH level.  As such, it is particularly useful for fish who prefer acidic water (eg angelfish).

Some fish, such as plecos, need wood as part of their natural diet.

Pieces of wood can provide excellent hiding places, prime spawning spots and natural territorial boundaries for fish.

Disadvantages:

Tannins will discolour water, turning it yellow-brown.  This usually fades over time.

It is necessary to soak or boil the wood to enable it to sink.  This can take weeks or even months.

Wood can harbour fish excrement, particularly underneath, which will need cleaning.

Lowering the pH is problematic for fish who enjoy a high pH (eg African cichlids).