  We consider a pair of smooth manifolds, which are the counterparts in the
even-dimensional and odd-dimensional cases. They are separately an almost
complex manifold with Norden metric and an almost contact manifolds with
B-metric, respectively. They can be combined as the so-called almost contact
complex Riemannian manifold. This paper is a survey with additions of results
on differential geometry of canonical-type connections (i.e. metric connections
with torsion satisfying a certain algebraic identity) on the considered
manifolds.
