One of the examples of R. Borcherds's product formulas is the following. Let $j(q) = q^{-1}+744+196884q+... = q^{-1}+744+\sum _{n=1}^\infty c(k)q^k$ be the ical modular function. Then for $0 < |p|, |q| \ll 1$ one has the equality $j(p) - j(q) = (p^{-1}-q^{-1})\prod _{k,l=1}^\infty (1-p^kq^l)^{c(kl)}$. In general, meromorphic ical modular forms of weight $1-n/2$ for $\mathrm {SL}(2, \mathbf {Z})$ with poles only at cusps produce meromorphic modular forms on Shimura varieties associated with the Lie group $O(2,n)$. We describe Borcherds's result and its recent applications.