Almost all shops (including grocery stores) are closed on Sundays, with the exception of some tourist shops. On Saturdays many small boutiques will close mid-afternoon. All major shopping centres are open until 20:00 from Monday to Saturday. Note that credit cards are not widely accepted; there's always an ATMs nearby however.

Marktstrasse (U-Bahn to Feldstrasse) is Hamburg's own Penny Lane. The street offers a wide variety of second-hand and boutique shops ranging from cheap to pricey and from retro to modern.
The "Designer Strip" on Neuer Wall (U-Bahn to Jungfernstieg) is lined with Cartier, Hermes and other elite stores - come armed with a credit card or husband.
Eppendorfer Baum, Eppendorfer Landstrasse, Lehmweg und Hegestrasse offer a multitude of up-scale boutiques and some great second-hand shops. A worthy trip for the serious shopper; U-Bahn to Eppenforfer Baum.