Typically, customs and import duties are the responsibility of the recipient but you should make your policy clear on your website so that shoppers know what they are liable for. Check with your local customs authority as the rules might be different if you are selling B2B.
Since the Trade and Cooperation Agreement came into force on 1 January, exports from the UK to the EU have been subject to harsher regulations causing confusion and frustration amongst retailers. Read the blog below in which we demystify some of the regulations around Brexit and UK to EU shipping.
Also, be sure to check that the goods you are selling are permitted to be imported to the destination. Some foodstuffs and live plants are not accepted into certain territories. And you may need to complete a customs declaration form to affix to your packages.