Who is considered party to a case? Who can become party to a case?

I assume bio mother and father are usually party to a case. Or, in my girl's case, only the bio mother is party to the case since bio dad has never been in the picture. So, can grandparents become party to the case if they live with bio mom? Can a new husband become party to the case if they got married after the kids were in care? Just wanted some clarification. Thanks!