bootstrap 4 styled select

The ability to style/format the select element is limited in general, not just in Bootstrap. That's why there are 3rd party plugins such as https://github.com/silviomoreto/bootstrap-select which utilize jQuery to convert an existing select element to "style and bring additional functionality to standard select elements".

You can also add some simple jQuery to make the Bootstrap dropdown behave like a select element: http://www.codeply.com/go/ganazCDXB5

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Update 2019 - Bootstap 4

Dropdown as Select: https://www.codeply.com/go/8bAECfv46k

SelectPicker plugin: https://www.codeply.com/go/zpZOlpB4GS

Multiselect plugin: https://www.codeply.com/go/UeqqALYwsT