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.
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