The quantum stochastic calculus initiated by \textit{R. L. Hudson} and \textit{K. R. Parthasarathy} [Commun. Math. Phys. 93, 301-323 (1984; Zbl 0546.60058)], and the noncausal stochastic calculus originating with the papers of \textit{M. Hitsuda} [Proc. 2nd Japan-USSR Symp. Probab. Theory 2, 111-114 (1972)] and \textit{A. V. Skorokhod} [Theory Probab. Appl. 20, 219- 233 (1975); translation from Teor. Veroyatn. Primen 20, 223-238 (1975; Zbl 0333.60060)], are two potent extensions of the Itô calculus, currently enjoying intensive development. The former provides a quantum probabilistic extension of Schrödinger's equation, enabling the construction of a Markov process for a quantum dynamical semigroup. The latter allows the treatment of stochastic differential equations which involve terms which anticipate the future. In this paper the close relationship between these theories is displayed, and a noncausal quantum stochastic calculus, already in demand from physics, is described.