SHELL

brew update

First update all package definitions (formulae) and Homebrew itself:
brew update

Upgrade everything with:
brew upgrade

You can now list which of your installed packages (kegs) are outdated with:
brew outdated

brew upgrade casks

for cask in `brew list --cask`; do
	brew upgrade --cask $cask;
done

# Or this shorthand
brew upgrade --cask $(brew list --cask)

brew update

brew update # Get most recent versions of available formulae and casks
brew outdated # Lists the outdated installed formulae and casks
brew upgrade # Upgrade the packages listed by brew outdated
brew upgrade <formula or cask> # Upgrade a specific formula or cask

brew update

#This updates homebrew itself.
brew update
#You can then upgrade all individual packages and formula with the following:
brew upgrade