A key issue in the development of heavy-ions drivers for inertial fusion is the feasibility of transporting and manipulating the required high beam currents without excessive particle loss and emittance growth. Experimental, theoretical and simulation studies at various laboratories have produced very encouraging results that have alleviated initial concerns on the current limits of periodic beam transport systems. The understanding and control of emittance growth is one of the dominant themes of current research. A brief overview of activities and recent achievements by the major groups working in this field will be presented. The new results on merging of multiple beamlets in the University of Maryland electron beam transport experiment will be discussed in more detail.