Selecting the right coils for wireless power transfer systems

Wireless Power Transfer Systems become more and more popular not only in the consumer area (charging of smartphones). There are two major system components, the power management ICs and the coils. One of the biggest challenges during development is that choosing not optimized coils can lead to lower efficiency, z-distance problems, heating effects, etc. What are the main design parameters to be considered when choosing an optimal Tx / Rx coil combination? There are several criteria depending on physics, power level, size and distance which impact the wireless power system.