How to Include HTML in Excerpts?

The excerpt is created in -> wp-includes/formatting.php with this code:

function wp_trim_excerpt($text) { // Fakes an excerpt if needed
    global $post;
    if ( '' == $text ) {
        $text = get_the_content('');
        $text = apply_filters('the_content', $text);
        $text = str_replace('\]\]\>', ']]>', $text);
        $text = strip_tags($text);
        $excerpt_length = 55;
        $words = explode(' ', $text, $excerpt_length + 1);
        if (count($words)> $excerpt_length) {
            array_pop($words);
            array_push($words, '[...]');
            $text = implode(' ', $words);
        }
    }
    return $text;
}

To change the behavior WP exhibits normally for excerpts, first remove this function (not from the core code, but using remove_filter() by placing this in your functions.php:

remove_filter('get_the_excerpt', 'wp_trim_excerpt');

Next, you’ll need to create a new function to control excerpts so you can copy the above function from WP core as a starting point. Name it something different. Then, change what you need. For example, if you want to allow the tag in your excerpts, you would modify this line:

$text = strip_tags($text);

to this:

$text = strip_tags($text, '<b>');

If you need more than one allowed html tag, list them after . So your new function in your functions.php might look like:

function nb_html_excerpt($text) {
    global $post;
    if ( '' == $text ) {
        $text = get_the_content('');
        $text = apply_filters('the_content', $text);
        $text = str_replace('\]\]\>', ']]>', $text);
        $text = strip_tags($text, '<b>');
        $excerpt_length = 55;
        $words = explode(' ', $text, $excerpt_length + 1);
        if (count($words)> $excerpt_length) {
            array_pop($words);
            array_push($words, '[...]');
            $text = implode(' ', $words);
        }
    }
    return $text;
}

And then finally, you need to tell WP to filter your excerpt through your new function. Add the filter like this in functions.php:

add_filter('get_the_excerpt', 'nb_html_excerpt');