In the process industry, it is crucial to ensure safety, high product quality, strict environmental compliance, and optimum economics. Among other important factors, this calls for high performance of the control loops. One of the main root caused for poor performance is control valve malfunctions. In particular, stiction is a long-standing valve problem in the process industry, causing limit cycles with a negative impact on process performance. Therefore, it is important to detect this phenomenon as early as possible, to distinguish it from other oscillation causes, to determine the correct maintenance measures, and, if applicable, to apply proper stiction compensation. The present survey covers the field of stiction modeling detection, and compensation, encompassing main research directions and significant contributions that have been reported in the literature. The relationship among different approaches is outlined showing their strengths and weakness. The review is complemented with a description of a academic commercial software packages that incorporate stiction diagnosis. Finally, a view on possible futrue research directions is provided.