The fifth generation (5G) network communication systems operate in the millimeter waves and are expected to provide a much higher data rate in the multi-gigabit range, which is impossible to achieve using current wireless services, including the sub-6 GHz band. In this work, we briefly review several existing designs of millimeter-wave phased arrays for 5G applications, beginning with the low-profile antenna array designs that either are fixed beam or scan the beam only in one plane. We then move on to array systems that offer two-dimensional (2D) scan capability, which is highly desirable for a majority of 5G applications. Next, in the main body of the paper, we discuss two different strategies for designing scanning arrays, both of which circumvent the use of conventional phase shifters to achieve beam scanning. We note that it is highly desirable to search for alternatives to conventional phase shifters in the millimeter-wave range because legacy phase shifters are both lossy and costly; furthermore, alternatives such as active phase shifters, which include radio frequency amplifiers, are both expensive and power-hungry. Given this backdrop, we propose two different antenna systems with potential for the desired 2D scan performance in the millimeter-wave range. The first of these is a Luneburg lens, which is excited either by a 2D waveguide array or by a microstrip patch antenna array to realize 2D scan capability. Next, for second design, we turn to phased-array designs in which the conventional phase shifter is replaced by switchable PIN diodes or varactor diodes, inserted between radiating slots in a waveguide to provide the desired phase shifts for scanning. Finally, we discuss several approaches to enhance the gain of the array by modifying the conventional array configurations. We describe novel techniques for realizing both one-dimensional (1D) and 2D scans by using a reconfigurable metasurface type of panels.