Strongly reflective modular forms and applications

We discuss two new classes of strongly reflective modular forms with respect to orthogonal groups $O(2,n)$. The first class contains 36 functions including the Borcherds form $\Phi_{12}$. The second one has at least 12 functions (this work is in progress) including the Igusa modular form of weight 5. We give some applications of these remarkable modular forms to the algebraic geometry of modular varieties and to the theory of Kac-Moody Lie algebras.