Optimize for mobile devices
Especially with more and more users viewing your Joomla website on mobile devices, you need to make sure it loads fast on those devices as well. While most desktop users in developed countries will have a broadband connection, this might not always be true for users on the go, with a 3G connection.
Even if you use a responsive template, the way the site is viewed adapts to to the screensize, but the resources that re loaded are the same as for the desktop user.
Make sure to keep this in mind. It takes some advanced techniques to cater for this, so this is a subject beyond the scope of Joomla-SEO.
User Agent Detection plugin
Just one tip for an extension that I found usefull is the User Agent Detection plugin developed by dutchman Rene Kreijveld. It detects whether you are on a desktop, phone or tablet. The feature works based on user agent. Though not 100% proof, this is a reliable method for mobile-detection. With some PHP knowledge you can then prevent modules or images from loading. So, it does not just HIDE, like what happens if you set a bootstrap-class of hidden-phone, but it exacually prevents loading and executing the whole module.
Example code: Only show module if user-agent tells you that we are NOT on a mobile device:
<?php if($ualayout != "mobile") {?
<jdoc:include type="modules" name="big-slider-module-x" style="xhtml" />
<?php } ?>
A similar plugin has been developed by Conflate, the Joomla Simple Mobile Detection plugin.
Advanced Module Manager
Another possibility is the use of the Nonumber extension Advanced Module Manager, which also works based on user-agent. It allows you to specify many parameters, including whether or not to load modules for mobile browsers: