SQL JOINS allow combining rows from multiple tables based on related columns. The main types of joins are inner joins, which return rows with matching values in both tables; left outer joins, which return all rows from the left table and matched rows from the right; right outer joins; and full outer joins. Functions in SQL allow manipulating data and include string, numeric, date, and conversion functions. Common functions are upper(), lower(), substr(), round(), greatest(), least(), and to_char() for conversions.