Aggregate function in an SQL update query?

I'm trying to set the value in one table to the sum of the values in another table. Something along these lines:

UPDATE table1
SET field1 = SUM(table2.field2)
FROM table1
INNER JOIN table2 ON table1.field3 = table2.field3
GROUP BY table1.field3

Of course, as this stands, it won't work - SET doesn't support SUM and it doesn't support GROUP BY.

I should know this, but my mind's drawing a blank. What am I doing wrong?

UPDATE t1
SET t1.field1 = t2.field2Sum
FROM table1 t1
INNER JOIN (select field3, sum(field2) as field2Sum
   from table2
  group by field3) as t2
on t2.field3 = t1.field3  

Use:

UPDATE table1
   SET field1 = (SELECT SUM(t2.field2) 
                   FROM TABLE2 t2 
                  WHERE t2.field3 = field2)

A good situation to use CROSS APPLY

UPDATE t1
   SET t1.field1 = t2.field2Sum
  FROM table1 t1
 CROSS APPLY (SELECT SUM(field2) as field2Sum
                FROM table2 t2
               WHERE t2.field3 = t1.field3) AS t2

Or you could use a mix of JBrooks and OMG Ponies answers:

UPDATE table1
   SET field1 = (SELECT SUM(field2)
                   FROM table2 AS t2
                  WHERE t2.field3 = t1.field3)
  FROM table1 AS t1

I know the question is tagged SQL Server but be careful with UPDATE with JOIN if you are using PostgreSQL. @JBrooks answer won't work :

UPDATE t1
SET t1.field1 = t2.field2Sum
FROM table1 t1
INNER JOIN (...) as t2
on t2.field3 = t1.field3  

You will have to adapt it to :

UPDATE table1 t1
SET t1.field1 = t2.field2Sum
FROM (...) as t2
WHERE t2.field3 = t1.field3  

See parameter from_list in the doc to get why FROM is considered by PostgreSQL as a self-join : https://www.postgresql.org/docs/9.5/static/sql-update.html#AEN89239

You can also use CTE like below.

;WITH t2 AS (
    SELECT field3, SUM(field2) AS field2
    FROM table2
    GROUP BY field3
)
UPDATE table1
SET table1.field1 = t2.field2
FROM table1
INNER JOIN t2 ON table1.field3 = t2.field3