For my own reference (and so whoever might find them useful). Sometimes just MySQL and sometimes in Laravel-esican.
Nullable integer column: Order numerically, except with NULL last
Source: http://stackoverflow.com/questions/2051602/mysql-orderby-a-number-nulls-last
MySQL
SELECT * FROM table ORDER BY ISNULL(field), field ASC;
Laravel
SomeModel::orderByRaw('ISNULL(field)')
->orderBy('field','ASC')
->get();
Regular integer column: Order numerically, except with ZEROs last
MySQL
SELECT * FROM table ORDER BY field!=0 DESC, field asc
Laravel
SomeModel::orderByRaw('field!=0 DESC')
->orderBy('field','ASC')
->get();
Order by, ignoring “the”
Laravel
$orderBy = DB::raw('CASE WHEN LEFT(`name`,4) ="The "
THEN REPLACE(`name`, "The ", "")
ELSE `name`
END');
SomeModel::orderBy($orderBy, 'ASC');