It is always demanding to learn robust visual representation for various learning problems; however, this learning and maintenance process usually suffers from noise, incompleteness or knowledge domain mismatch. Thus, robust representation learning by removing noisy features or samples, complementing incomplete data, and mitigating the distribution difference becomes the key. Along this line of research, low-rank modeling has been widely-applied to solving representation learning challenges. This survey covers the topic from a knowledge flow perspective in terms of: (1) robust knowledge recovery, (2) robust knowledge transfer, and (3) robust knowledge fusion, centered around several major applications. First of all, we deliver a unified formulation for robust knowledge discovery given single dataset. Second, we discuss robust knowledge transfer and fusion given multiple datasets with different knowledge flows, followed by practical challenges, model variations, and remarks. Finally, we highlight future research of robust knowledge discovery for incomplete, unbalance, large-scale data analysis. This would benefit AI community from literature review to future direction.