Matt Wiebe

WordPress 3.4 introduced native Twitter embeds. You may not want to use these for privacy–or other–reasons, while still allowing for other embeds. This plugin disables only Twitter embeds.

Disable Twitter Embeds

Disable the native Twitter embeds introduced in WordPress 3.4.

Embedly

Enhance the default WordPress embedding to get previews for any article, 
including your own blog posts. You also get embeds for Gfycat, Twitch, Google 
Maps, and Embedly’s growing list of <a href="http://embed.ly/providers" rel="nofollow ugc">500+ supported 
providers</a>.
You can customize the style of the embeds, to optimize for darker WP themes, 
alignment, and width. In addition, social buttons can be added around the embeds 
to make it easier to share content from your blog posts.
If you have an Embedly Cards account, you can link it to the plugin with your Embedly API key. Not only does this remove branding from the cards, it also gives you access to analytics and viewer behaviors for most popular music and video player embeds (YouTube, Vimeo, Instagram, SoundCloud). Find out how many people viewed your embeds for how long. To learn more about Embedly Cards please visit <a href="http://embed.ly/cards" rel="nofollow ugc">our website</a>.
Using it is as simple as the default WordPress embedding. Embed media by pasting its URL in a single line when writing a post
The plugin automatically displays an embed of the media in the WordPress post 
editor (for WP 4.0+).
Fair Warning: This plugin generates static HTML content for your posts. After you deactivate 
the plugin, that HTML will still remain behind in all posts where the plugin was used to create 
embeds.

The Embedly Plugin extends Wordpress's auto-embed feature to give your blog more media types and style optons.

Disable Twitter Embeds vs Embedly