I'm currently using the following PHP code:

    // Get all subordinates
    $subords = array();
    $supervisorID = $this->session->userdata('supervisor_id');
    $result = $this->db->query(sprintf("SELECT * FROM users WHERE supervisor_id=%d AND id!=%d",$supervisorID, $supervisorID));
    $user_list_query = 'user_id='.$supervisorID;
    foreach($result->result() as $user){
        $user_list_query .= ' OR user_id='.$user->id;
        $subords[$user->id] = $user;
    }

    // Get Submissions
    $submissionsResult = $this->db->query(sprintf("SELECT * FROM submissions WHERE %s", $user_list_query));
    $submissions = array();
    foreach($submissionsResult->result() as $submission){
        $entriesResult = $this->db->query(sprintf("SELECT * FROM submittedentries WHERE timestamp=%d", $submission->timestamp));
        $entries = array();
        foreach($entriesResult->result() as $entries)   $entries[] = $entry;
        $submissions[] = array(
            'user' => $subords[$submission->user_id],
            'entries' => $entries
        );
        $entriesResult->free_result();
    }

Basically I'm getting a list of users that are subordinates of a given supervisor_id (every user entry has a supervisor_id field), then grabbing entries belonging to any of those users.

I can't help but think there is a more elegant way of doing this, like SELECT FROM tablename where user->supervisor_id=2222

Is there something like this with PHP/MySQL?
Should probably learn relational databases properly sometime. :(