What is the latest drush version and how do I install it?
drush dl was never supposed to be used to download Drush. It happens to work because Drush is hosted on drupal.org as module, but the latest development are done on github.com. On drupal.org, you find just old versions, dated 2013.

As per July 17, 2016, the latest version is 8.1.2. You can install it using Composer, if you are using any Linux OS, or OS X, and in this case it is easy as running the following command:

composer global require drush/drush:~8


Don't forget to add ~/.composer/vendor/bin to your shell PATH variable, or the shell will not find Drush's executable.