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Users of WordPress.com, we bring you good news! You can now embed Pens in your blog posts (and pages) there!
This is because CodePen supports oEmbed - and WordPress.com was gratious enough to whitelist CodePen to work there. Big thanks to Joey Kudish and the WordPress.com for helping us get that working well.
Users of self-hosted WordPress sites (WordPress.org), never fear, we're told this is likely going to be in Jetpack soon so oEmbed-style embeds will work there too. But you don't have to wait! There is a plugin that enables support right now. And of course you could just use the regular embed code (see docs) for embedding Pens as well (which allows for powerful features like theming and adjusting the height and such).