Are shops and museums open on Sunday in Belgium?

I'll speak for Brussels where I live :

• Most museums are open on Sundays, as are they in every place I've been to in the EU (including the Netherlands). Most countries strive to make culture and arts accessible to people. You don't do that by opening only on working days.
• As a result, most tourist shops and businesses selling food and beverages around landmarks, museums and monuments will be open.
• People like their Sunday family lunchs, so small stores selling fresh products (bakery, grocery, butcher's) are often open in the morning. Sunday is a big day for many restaurants and bistrots as well.
• Some supermakets (not all of them) are open in the morning.
• Some shopping malls are open at special times of the year : Christmas season, January sales, etc.

So Sundays are definitely not dead days, especially if you're planning to do tourist oriented stuff. I wouldn't claim it's the case in every small Belgian village, but certainly so in big cities and touristic ones.

There's an excellent summary of the hours available, which also links to the official regulation (in Dutch/Flemish if you can read that).

The basic summary is:

• You can be open any day during 'shopping hours' - between 0500 and 2100.
• a shop owner is required to have a 24 hour 'day of rest' every week. Most choose to do it on Sundays.
• However, you can't employ personnel on Sundays, so generally smaller businesses might be open.
• There are exceptions - bakeries, tourist shops...

There have been several attempts at further legislation, all described on that same page.

For Flanders you can more or less compare it the Netherlands. There are some small differences though.

1. Bakeries. Where in the Netherlands you will not be able to find a bakery on a Sunday, in Belgium they are all open on Sunday.
2. some DIY shops are usually also open on Sunday in Flanders.
3. The Netherlands has more so-called buying sundays ("koop-zondag", then Belgium. Things are changing for the better where more and more shopping centers are opening on sunday as well. There is a political discussion going on to open up touristic city centers on every sunday, resembling the policy in the Netherlands.