This feature is available in Site Explorer: Organic Keywords, Calendar > Positions reports, and in Rank Tracker: Overview, Ranking History, and Metrics reports.

In each of these reports, click on the dropdown with a squiggly graph icon:

You'll open up the Position History graph that shows ranking URLs, the date, and the position they ranked for this keyword. There are a number of actions you can take:

Use the date filter to select a time frame:

Or, click and drag on the chart itself to select a custom date range:

You can filter to see movements of ranking URLs across only the top 10, 20, 50 or 100 positions in Google.

Here's an example where the Top 10 filter is selected:

Ahrefs annotates updates made in Ahrefs or Google that may have an impact on rankings. At the bottom on the graph, you can hover over the "G" or "a" bubbles for more information about the update made on that day:

And you can choose to toggle them off if you don't wish to see them in the graph:

Clicking the button Export button will immediately start a download in your browser's default downloads folder. The dates are in the rows, and the ranking URLs are in the columns:

Click on the caret next to ranking URLs to open the URL menu with relevant SEO statistics, as well as shortcuts to different Site explorer reports for the target ranking URL.

Click on the “Add domain to compare” button to enter domains or other URLs for comparison, and apply modes to them to refine the results.

Once added, you can see the line drawn in the graph for the new added URL, and follow its position history aside the other ranking URLs:

This feature is available in Site Explorer: Paid Keywords

In this account, click on the dropdown with a squiggly graph icon:

You'll open up the Ads Position History graph.

By hovering over the the coloured bars, you'll be able to see the Ad's title, copy text, link, and date it was found in the SERPs.

Similar to Positions history graph, you can also select a date range adjust how far back to view Ads position history:

Clicking on the caret next to ranking URLs also opens the URL menu with relevant SEO statistics, as well as shortcuts to different Site explorer reports for the target ranking URL: