  Many distinct problems give birth to Darboux-Halphen system of differential
equations and here we review some of them. The first is the classical problem
presented by Darboux and later solved by Halphen concerning finding infinite
number of double orthogonal surfaces in $\mathbb{R}^3$. The second is a problem
in general relativity about gravitational instanton in Bianchi IX metric space.
The third problem stems from the new take on the moduli of enhanced elliptic
curves called Gauss-Manin connection in disguise developed by one of the
authors and finally in the last problem Darboux-Halphen system emerges from the
associative algebra on the tangent space of a Frobenius manifold.
