Transformers used in electrical power transmission are rife with issues that can cause energy losses between the two coils. When explaining these energy losses I am going to assume you aware of how transformers work.
Heat loss is the most common form of energy loss in a transformer. Since there is an electrical current in both the primary and secondary coils of the transformer, energy will be used to overcome resistance in the wires. This energy is transformed into heat which escapes from the coils resulting in the energy loss. In order to minimise the energy loss, the coils should be made from a good conducting material such as copper, and the wires should have a large cross-sectional area to minimise resistance.
Eddy currents result in heat loss as well, but through a different method. When the primary coil induces an alternating magnetic field, the field passes through the transformer core. This induces small alternating currents in the core, which cause heat loss exactly as explained earlier. To minimise losses due to eddy currents, you will have to laminate the core material. This involves cutting up the core into separate strips, and placing strips of an insulating material between the strips of the core material. The insulator has no effect on the magnetic field through the core, but reduces the size of the eddy currents themselves.
Hysteresis losses are also caused by the magnetic field through the core. When the magnetic field passes through the core material, the core itself becomes magnetic with a north and south pole. As the magnetic field alternates and changes direction, the poles of the core swap ans the core isn't a permanent magnet. The energy loss occurs because once the core material has been magnetised in one direction, it resists being magnetised in another direction, meaning that extra energy is needed to remagnetise the core.The only way to minimise this energy loss is to make sure that the core of the transformer is made from a 'soft' magnetic material such as iron, which is less resistant to being magnetised
Finally, energy is also lost through flux losses. When the primary coil generates an alternating magnetic field, it also generates flux. Unfortunately, not all of the flux is linked from the primary coil to the secondary coil, which results in not all of the field generated being channelled through the core into the secondary coil. In order to minimise the energy lost through flux losses, the secondary coil should be wound around the primary coil in order to reduce loss of flux linkage.