What are the advantages and disadvantages of dual-wielding?

For weapons:
Pros:

  • can get up to 4 weapon effects onto a pair of weapons.
  • More DPS as you attack faster with duel wielding perks

Cons:

  • can't block
  • can't bash (shields/two handed weapons lets you bash)
  • need to find two good weapons instead of one

For dual casting spells, you'll want to look here.