Where can I see the emails I have sent?

Short answer: Open Promotions, tab “Send History”. The list keeps sends made with a template; emails sent without one do not appear there.

Steps

Open the Promotions page of the dashboard, then the “Send History” tab.
For each send the list gives the subject, who sent it, the number of recipients, the progress and the status.
Click a row to open its detail on the right-hand side.

What the list holds, and what it does not

The tab's own heading says it: “History of Emailings Sent with an Email Template”.

An email sent with a template stays there permanently, even if the template has since been deleted.
An email sent without a template only appears while it is still scheduled, long enough for you to cancel it. Once it goes out, it drops off. Those rows carry a chip reading “Individual email” or “Support reply”.

The six tracking figures

The detail shows a progress bar and six counters: Sent, Delivered, Opened, Clicked, Failed and Bounced. A seventh, Excluded, counts the contacts dropped before the send.

These figures come in over the following hours: an email opened tomorrow moves the counter tomorrow.

The “Opened” count is not 100% reliable

This counter relies on an invisible image that the recipient's email client loads when the message is displayed. It is wrong in both directions:

it counts too few — many email clients block images by default: the person reads your email, the image is never loaded, the open is never counted;
it counts too many — other clients, and some companies' security filters, load images and follow links automatically, before anyone has opened the message. The open is counted, and sometimes the click with it.

On top of that, an open can be inferred: a click or a spam report counts as one, since the email had to be opened to get that far.

So read “Opened” as a trend from one send to the next, not as a number of people. Delivered, Failed and Bounced are reported by the server receiving the message: those do not depend on how the email client behaves.

The statuses of a send

Pending, Scheduled, Sending, Completed, Canceled. A scheduled send is canceled from its detail; the others can be deleted from the history.

Going further

You'll know it worked when: The emailing appears in the list with its status, and its detail shows the tracking recipient by recipient.