This paper presents a framework of current problems and related literature on Internet/web surveys. It proposes a new classification of research topics on challenging issues. Thereby it takes into account application the role that these surveys play in different research contexts (official statistics, academic research, market research). In addition critical research, open questions and trends are identified. Furthermore a specific section is devoted to bias estimation, which is a critical point in this type of survey. In particular, original bias and variance definitions are proposed.