  The classification of reflective modular forms is an important problem in the
theory of automorphic forms on orthogonal groups. In this paper, we develop an
approach based on the theory of Jacobi forms to give a full classification of
2-reflective modular forms. We prove that there are only 3 lattices of
signature $(2,n)$ having 2-reflective modular forms when $n\geq 14$. We show
that there are exactly 51 lattices of type $2U\oplus L(-1)$ which admit
2-reflective modular forms and satisfy that $L$ has 2-roots. We further
determine all 2-reflective modular forms giving arithmetic hyperbolic
2-reflection groups. This is the first attempt to classify reflective modular
forms on lattices of arbitrary level.
