The basic physical problems determining the fusion prospects of open traps are considered. Main attention is paid to the possibility of a scalable modelling of the anomalous transverse transport in long solenoids (which are a necessary component of most of the types of open traps), and to the problem of the MHD stability of axisymmetric ambipolar traps. The experimental device for studying the transverse transport in a long solenoid, based on the concept of a gas-dynamic trap, is described. Various axisymmetric MHD-stabilizers for ambipolar traps-are considered, including the recently suggested stabilizer in the form of a 'fat' mirror machine. Such a stabilizer is shown to provide the suppression of large-scale flute perturbations in the framework of a 'natural' geometry of open traps.