  Angular momentum transport is one of the cornerstones of spintronics. Spin
angular momentum is not only transported by mobile charge carriers, but also by
the quantized excitations of the magnetic lattice in magnetically ordered
systems. In this regard, magnetically ordered insulators provide a platform for
magnon spin transport experiments without additional contributions from spin
currents carried by mobile electrons. In combination with charge-to-spin
current conversion processes in conductors with finite spin-orbit coupling it
is possible to realize all-electrical magnon transport schemes in thin film
heterostructures. This review provides an insight into such experiments and
recent breakthroughs achieved. Special attention is given to charge current
based manipulation via an adjacent normal metal of magnon transport in
magnetically ordered insulators in terms of spin-transfer torque. Moreover, the
influence of two magnon modes with opposite spin in antiferromagnetic
insulators on all-electrical magnon transport experiments is discussed.
