  We study Morita rings $\Lambda_{(\phi,\psi)}=\bigl({smallmatrix} A
&_AN_B_BM_A & B {smallmatrix}\bigr)$ in the context of Artin algebras from
various perspectives. First we study covariant finite, contravariant finite,
and functorially finite subcategories of the module category of a Morita ring
when the bimodule homomorphisms $\phi$ and $\psi$ are zero. Further we give
bounds for the global dimension of a Morita ring $\Lambda_{(0,0)}$, regarded as
an Artin algebra, in terms of the global dimensions of $A$ and $B$ in the case
when both $\phi$ and $\psi$ are zero. We illustrate our bounds with some
examples. Finally we investigate when a Morita ring is a Gorenstein Artin
algebra and then we determine all the Gorenstein-projective modules over the
Morita ring with $A=N=M=B=\Lambda$, where $\Lambda$ is an Artin algebra.
