How do I update Drupal core on composer install? [duplicate]

Question

I installed (or downloaded) drupal 8 via:

composer create-project drupal/drupal my_site_name 8.0.*

Which, at the time I ran it, downloaded Drupal 8.0.1. Now drupal 8.0.2 is available and I'd like to update to this version.

I'm not sure how to update core but I decided to try running composer update from my drupal site's root directory.

This updates many packages (e.g.):

$ composer update
Loading composer repositories with package information
Updating dependencies (including require-dev)
  - Removing composer/installers (v1.0.21)
  - Installing composer/installers (v1.0.22)
    Loading from cache

> Drupal\Core\Composer\Composer::vendorTestCodeCleanup
  - Removing symfony/class-loader (v2.7.6)
  - Installing symfony/class-loader (v2.7.9)
    Downloading: 100%

> Drupal\Core\Composer\Composer::vendorTestCodeCleanup
  - Removing symfony/console (v2.7.6)
  - Installing symfony/console (v2.7.9)
    Downloading: 100%

(...)

> Drupal\Core\Composer\Composer::vendorTestCodeCleanup
  - Removing twig/twig (v1.23.1)
  - Installing twig/twig (v1.23.3)
    Downloading: 100%

However I don't see anything about updating drupal/drupal. And when I visit my site's status report it still shows 8.0.1.

So how do I actually update core via composer?