The Sensor Web vision refers to the addition of a middleware layer between sensors and applications. To bridge the gap between these two layers, Sensor Web systems must deal with heterogeneous sources, which produce heterogeneous observations of disparate quality. Managing such diversity at the application level can be complex and requires high levels of expertise from application developers. Moreover, as an information-centric system, any Sensor Web should provide support for Quality of Observation (QoO) requirements. In practice, however, only few Sensor Webs provide satisfying QoO support and are able to deliver high-quality observations to end consumers in a specific manner.This survey aims to study why and how observation quality should be addressed in Sensor Webs. It proposes three original contributions. First, it provides important insights into quality dimensions and proposes to use the QoO notion to deal with information quality within Sensor Webs. Second, it proposes a QoO-oriented review of 29 Sensor Web solutions developed between 2003 and 2016, as well as a custom taxonomy to characterise some of their features from a QoO perspective. Finally, it draws four major requirements required to build future adaptive and QoO-aware Sensor Web solutions.