This talk will discuss some recent results on constructing quaternionic and Clifford algebraic coherent states. This construction generalizes, to matrix domains, the well known construction of coherent states on complex domains. The resulting vector valued coherent states have potentially interesting physical applications, especially in atomic physics, e.g., in the study of the spectra of Jaynes-Cummings type of Hamiltonians. The talk will also explore other theoretical aspects of these vector coherent states, such as their relation to families of orthogonal polynomials.