To start with, there are some basics:

• No backgrounds or background images can be used on any eBook that will be converted into Kindle (Mobi) format. While this feature/formatting is supported in what's called "KF8" formatting (the more-advanced formatting that was introduced with the Kindle Fire devices), the restrictions still hold for the older devices.  See below about how this can be addressed.  
• Text boxes or pull-quotes will have to be formatted (generally) differently than in print.
• Images in Kindle e-ink volumes can't be wrapped inside paragraphs, but can have this in ePUB format.  Again, this is now supported in KF8 format, but not KF7 (for the older e-ink devices, and the Kindle for iPad/iPhone reader).  
• You can’t put text over an image in an Amazon eBook.  This is true unless a book is being made in "Fixed-Format," see our article about this:  Fixed-Format eBooks
• You can only use tables that are about 3 columns wide, and very few rows.  This is still true, as of 2015.  
   

For most things, you can only have a single column of text.  No “newspaper-like" columns.   (see the Figures below:  Sample of Kindle e-ink device text, Font Size 1 and then the same exact book "page" in Font Size 8)  Some small areas with two column items can sometimes be made to look right by using tables, but this formatting trick needs to be used sparingly. 

Many graphic elements, like characters from foreign languages, can’t be used.  Generally, we recommend that most indices be omitted, or simply entered without page numbers.  Almost every eBook reader out there has a great search function.  This makes it better for your readers and less expensive for you!