How do I concatenate row-wise instead of column-wise?

I have a table like this:
SELECT * FROM old_tab;
id | descr
-------------------
1 | aaa
1 | aaa
1 | bbb
2 | ccc
2 | bbb
3 | ddd
3 | ddd
3 | eee
3 | fff
4 | bbb
etc...

And I want a new table where the descr is concatenated row-wise like this:
SELECT * FROM new_tab;
id | descr
--------------------------
1 | aaa;bbb
2 | ccc;bbb
3 | ddd;eee;fff
4 | bbb
etc...

This is the closest I get....:
UPDATE new_tab SET descr = old_tab.descr||' ; '||old_tab.descr from
old_tab where old_tab.id=new_tab.id;
UPDATE 4
SELECT * FROM new_tab ;
id | descr
----+-----------
1 | aaa ; aaa
2 | ccc ; ccc
3 | ddd ; ddd
4 | bbb ; bbb
etc...

Thus, the concatenating operator never works on other rows than the
present. How can I get around that and still stick to the postgresql syntax?

Regards
Marcus