MySQL: ALTER COLUMN vs CHANGE vs MODIFY COLUMN

ALTER COLUMN
Used to set or remove the default value for a column. Example:-

ALTER TABLE MyTable ALTER COLUMN foo SET DEFAULT ‘bar’;
ALTER TABLE MyTable ALTER COLUMN foo DROP DEFAULT;

CHANGE COLUMN
Used to rename a column, change its datatype, or move it within the schema. Example:-

ALTER TABLE MyTable CHANGE COLUMN foo bar VARCHAR(32) NOT NULL FIRST;
ALTER TABLE MyTable CHANGE COLUMN foo bar VARCHAR(32) NOT NULL AFTER baz;

MODIFY COLUMN
Used to do everything CHANGE COLUMN can, but without renaming the column. Example:-

ALTER TABLE MyTable MODIFY COLUMN foo VARCHAR(32) NOT NULL AFTER baz;
The official documentation for ALTER TABLE (for MySQL 5.1) is here.