Non-orthogonal multiple access (NOMA) has received an enormous attention in the recent literature due to its potential to improve the spectral efficiency of wireless networks. For several years, most of the research efforts on the performance analysis of NOMA were steered towards the ergodic sum rate and outage probability. More recently, error rate analysis of NOMA has attracted massive attention and sparked massive number of researchers whose aim was to evaluate the error rate of the various NOMA configurations and designs. Therefore, the large number of publications that appeared in a short time duration made highly challenging for the research community to identify the contribution of the different research articles. Therefore, this work aims at surveying the research work that considers NOMA error rate analysis and classifying the contributions of each work. Therefore, work redundancy and overlap can be minimized, research gabs can be identified, and future research directions can be outlined. Moreover, this work presents the principles of NOMA error rate analysis.