Many countries have experienced a surge in the level of the penetration of solar PV systems in the last decade. A huge portion of the newly deployed PV systems are connected to low voltage Grid. High Penetration of PVs at this level could potentially disrupt the normal operation of distribution network. A major concern is the impact of these units on power quality indices. Namely, photovoltaic panels could increase the level of voltage and current unbalance, deteriorate harmonic distortion and cause the voltage rise. These concerns may prohibit higher pentation levels of PVs. Thus, proper assessment techniques are vital for network operators for the planning and decision-making process. On the other hand, many characteristics of PV system are inherently uncertain. These uncertainties should be properly modeled in assessment framework. The main effort of research communities is to propose new methodologies that could model the uncertainty of solar power generation and stochastic assessment methods that could accurately estimate the state of the operation of the network with different levels of penetration of solar photovoltaics. This paper provides a comprehensive review of recent publications and trend of research activities regarding methods of representing uncertain variables and stochastic assessment techniques for power system quality analysis.