In this article we study the bilinear maps of algebras which are zero on elements with zero products and we present the notion of zero product determined algebra. Then we review some results about this notion. More precisely, first we study the properties of zero product determined algebras, then we will give some algebras which are non-zero product determined or zero product determined algebras, especially we will examine whether some nest algebras on a Banach or Hilbert space is zero product determined. Also we introduce some related open problems.
