Various formulations of the coupled equations in the quantum theory of atom-diatom reactive scattering—based on the ordinary Schrödinger equation and on the generalized equations of the arrangement channel quantum mechanics—are summarized with emphasis on symmetry properties of these formulations. New simplified and/or symmetrized versions are presented of the coupled ordinary differential equations derived previously (using the mixed Jacobi/hyperspherical coordinates) from the two distinct generalized Schrodinger equations which incorporate the arrangement channel permuting and the Fock arrangement coupling scheme, respectively. Inhomogeneous coupled equations arising from the close-coupling description of some related half-collision processes are also included in the considerations. Numerical approaches to solution of the coupled equations problems are recapitulated. The log-derivative method is presented in various versions. The material included in the presentation supplements previous reviews on numerical methods for molecular scattering calculations in that: (i) more information is given on implementations of the invariant imbedding technique; and (ii) determination of scattering wave functions and evaluation of some first- and second-order transition amplitudes involving these functions are considered in addition to determination of the scattering matrices.