You can download CSV exports on media blocks (like the Most recent media), they include all media analytics and information (media type, caption, likes, comments...) and even the Instagram URL of the media!

You can get all posts within a certain date range by using the Global Date-picker and sort the data by media type and several other options. 

Note that this option is only available for the ELITE, MASTER, PRO and ADVANCED users.

In order to export it, choose the feature and the date you are interested in and click on the grey arrow on the right-hand side of the block as shown below:

Also known as "How do I download the data for my media performance by post"