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This paper surveys the optimization frameworks and performance analysis methods for large intelligent surfaces (LIS), which have been emerging as strong candidates to support the sixth-generation wireless physical platforms (6G). Due to their ability to adjust the behavior of interacting electromagnetic (EM) waves through intelligent manipulations of the reflections phase shifts, LIS have shown promising merits at improving the spectral efficiency of wireless networks. In this context, researchers have been recently exploring LIS technology in depth as a means to achieve programmable, virtualized, and distributed wireless network infrastructures. From a system level perspective, LIS have also been proven to be a low-cost, green, sustainable, and energy-efficient solution for 6G systems. This paper provides a unique blend that surveys the principles of operation of LIS, together with their optimization and performance analysis frameworks. The paper first introduces the LIS technology and its physical working principle. Then, it presents various optimization frameworks that aim to optimize specific objectives, namely, maximizing energy efficiency, sum-rate, secrecy-rate, and coverage. The paper afterwards discusses various relevant performance analysis works including capacity analysis, the impact of hardware impairments on capacity, uplink/downlink data rate analysis, and outage probability. The paper further presents the impact of adopting the LIS technology for positioning applications. Finally, we identify numerous exciting open challenges for LIS-aided 6G wireless networks, including resource allocation problems, hybrid radio frequency/visible light communication (RF-VLC) systems, health considerations, and localization.