In this survey we establish bijective correspondences between the following classes of objects: (1) \beta_{-1} and \{ \beta_n \}_{n=0}^{\infty} , with \beta_n \in \mathbb C^{p \times p} for n=-1,0,\ldots , \beta_{-1} unitary, \| \beta_j \| < 1 for j \geq 0 and \sum_{j=0}^{\infty} \| \beta_j \| < \infty ; (2) A unitary matrix \beta_{-1} \in \mathbb C^{p \times p} and a spectral density \Delta belonging to the Wiener algebra \mathcal W^{p \times p} with \Delta(\zeta) \succ 0 for all \zeta on the unit circle \mathbb T ; (3) CMV matrices based on a unitary matrix \beta_{-1} \in \mathbb C^{p \times p} and a spectral density \Delta that meets the constraints in (2); (4) scattering matrices that belong to the Wiener algebra \mathcal W^{p \times p} ; (5) a class of solutions of an associated matricial Nehari problem. The bijective correspondence between summable sequences of contractions and positive spectral densities in the Wiener algebra \mathcal W^{p \times p} (i.e., between class (1) and class (2)) is known as Baxter's theorem and was established by Baxter when p=1 and Geronimo when p \geq 1 . The connections between CMV matrices, the solutions of a related Nehari problem and an inverse scattering problem seem to be new when p > 1 . There is partial overlap of the connection between the considered Nehari problem and a discrete analogue of an inverse scattering problem considered by Krein and Melik-Adamjan. de Branges spaces of vector-valued polynomials are used to ease a number of computations.