Here are my favourite online retailers, I've been wanting to offer a curated list so you have a point of reference. (I also spend a lot of time going through sales for that elusive item that escaped me the first time around).

Most retailers nowadays will ship all over the world, but they charge fees so it's quite inconvenient. I've separated between US/Europe so you know where they are based and what to expect. The global ones are listed first

Amazon
ASOS (Fashion)
Ebay (Fashion, Beauty, Technology...)
Farfetch (Fashion)
FreePeople (Fashion)
H&M (Fashion)
Net-A-Porter (Fashion & Beauty)
Mytheresa (Fashion)
Moda Operandi (Fashion)
Shopbop (Fashion)
Ssense (Fashion)

USA

Avenue 32 (Fashion)
Beautylish (Beauty)
Bergdorf Goodman (Fashion & Beauty)
La Garconne (Fashion)
Nordstrom (Fashion & Beauty)
Neiman Marcus (Fashion & Beauty)
Barneys New York (Fashion & Beauty)
Sephora (Beauty)
Fashionphile (Second hand Bags and Accesories)
Forward by Elyse Walker (Fashion)
TheRealReal (Second hand Bags and Accesories)
Revolve Clothing (Fashion)
Ssense (Fashion)
Stuart Weitzman (Shoes)
The Dreslyn (Fashion)
The Reformation (Fashion)
Topshop (Fashion)
Vince (Fashion)
Yoox (Fashion)
Zappos (Fashion)
Zimmermann (Fashion & Swimwear)

Europe & Rest of the World

CultBeauty (Beauty)
Free People (Fashion)
Stuart Weitzman (Shoes)
Vestiare Collective (Second hand Fashion)
Vide-Dressing (Second hand Fashion)
Feel Unique (Beauty)
Harvey Nichols (Fashion & Beauty)
Look Fantastic (Beauty)
Luisa Via Roma (Fashion)
Matchesfashion (Fashion)
Topshop (Fashion)
Selfridges (Fashion & Beauty)
Yoox (Fashion)
Zalando (Shoes)