Christian Louboutin for anyone who doesn't know, is a French
designer of luxury footwear and handbags, whose best-known goods
are high-heeled (often very!) women's shoes. From the mid-1990s
onwards, he has added to the shoes an outer sole in a red colour
which is a specific pantone shade. The shoes are worn by
celebrities and were a favourite of Carrie in Sex and The City. The
colour, applied to the sole of a high-heeled shoe, is registered as
a Benelux trade mark as of 2005 and the EU since 2016 (filed in
2010, so it took a while!).

The above image is the EU registration image for high-heeled
shoes in Class 25.
In December 2022, the Court of Justice of the European Union
(CJEU) held that, retailing giant Amazon could be held liable in
relation to advertisements on its online platform selling
'fake' Christian Louboutin branded shoes. I have dug a
little more into the case below and the background to the
dispute.