  We briefly review the five possible real polynomial solutions of
hypergeometric differential equations. Three of them are the well known
classical orthogonal polynomials, but the other two are different with respect
to their orthogonality properties. We then focus on the family of polynomials
which exhibits a finite orthogonality. This family, to be referred to as the
Romanovski polynomials, is required in exact solutions of several physics
problems ranging from quantum mechanics and quark physics to random matrix
theory. It appears timely to draw attention to it by the present study. Our
survey also includes several new observations on the orthogonality properties
of the Romanovski polynomials and new developments from their Rodrigues
formula.
