Being the first unitary representation in the discrete series for the Virasoro algebra, the Virasoro vertex operator algebra L(1/2,0) over complex field and its representation theory is the foundation of the framed vertex operator algebras, and plays important rules in studying the Frenkel-Lepowsky-Meurman's moonshine vertex operator algebra and in classification of holomorphic vertex operator algebras with small charge charges. We prove recently that L(1/2,0) has a Z[1/2]-form which produces a modular Virasoro vertex operator algebra over any algebraically closed field whose characteristic is different from 2. If the characteristic of the field is not 7, this modular vertex operator algebra is rational in the sense that the modular category is semisimple. This leads to a theory of modular framed vertex operator algebras. Furthermore, a Z[1/2]-form for any framed vertex operator algebra over C is constructed, and a modular framed vertex operator algebra is obtained from any framed vertex operator algebra over C. If the characteristic of the field is 7, this simple modular vertex operator algebra is generated by two vectors and has exactly three inequivalent irreducible modules. This is a joint work with Ching-Hung Lam and Li Ren.