One-handed weapons can be equipped to either your right or left hands. When wielding two weapons, you can perform special power attacks, but cannot block.

The one handed Perk Dual Savagery gives 50% bonus dmg to Dual Wielding Power Attacks.

The one handed Perk Dual Flurry increases the speed of your dual wielding attacks.

Spells can also be equipped to either hand. Some Perks give you the ability to Dualcast (cast the same spell with both hands simultaneously) for a stronger effect.

The following Perks and Spells benefit from Dualcasting:

Restoration
Restoration Dual Casting - Allows you to cast a more powerful version of a restoration spell

Destruction
Destruction Dual Casting - Overcharges the Destruction Spell for more damage
Impact - Cause dual cast spells to stagger the opponent

Conjuration
Conjuration Dual Casting - Increases duration of dual cast spells

Illusion
Illusion Dual Casting - Lets you cast more powerful versions of illusion spells

Alteration
Alteration Dual Casting - Overcharge your alteration spell and create a stronger version when you dualcast