Ideally I would like to be able to reference later what I've completed to date, but I can't seem to see where any of that is stored.
On a free account, you can enter a project and click on the circular icon in the bottom-right corner to see all tasks completed within this project.
On a Premium account, you can click on the Karma score in the top-right corner go to "View all completed" and see all completed tasks from all projects in one place, incl. completion events of recurring tasks, sorted by date, time with the option to filter the list by time, project, label or visualize your productivity with graphs and charts.
I don't see a circular icon on the iPhone or the iPad when I am in the projects view....should I?
Unfortunately, this option is only available on the web, you can't see completed tasks through our mobile apps. We will consider adding such option in the future, though and you're welcome to vote for this request in our Votebox: http://todoist.com/Vote_iOS/showProposal/7/
You have to add this option thats why i bought the premium version.