Quite a chunk of the HTML output of your WordPress site comes not from your theme but from the bowels of the WordPress core.
A combination of WordPress’ age and a necessary requirement for backwards compatibility, some of that markup is decidedly old-fashioned.
If you want truly responsive and flexible images and embeds, you need to get modern and semantic.
In version 3.6, WordPress added Semantic Markup as a theme feature. This allowed any theme to generate updated markup when calling functions such as wp_list_comments, comment_form and get_search_form.
Version 3.9 added two more options to Semantic Markup, gallery and caption, which updates the generated HTML for images and galleries.