Summary: The paper gives an overview of various methods for identifying dynamic errors-in-variables systems. Several approaches are classified by how the original information in time-series data of the noisy input and output measurements is condensed before further processing. For some methods, such as instrumental variable estimators, the information is condensed into a nonsymmetric covariance matrix as a first step before further processing. In a second class of methods, where a symmetric covariance matrix is used instead, the Frisch scheme and other bias-compensation approaches appear. When dealing with the estimation problem in the frequency domain, a milder data reduction typically takes place by first computing spectral estimators of the noisy input-output data. Finally, it is also possible to apply maximum likelihood and prediction error approaches using the original time-domain data in a direct fashion. This alternative will often require quite high computational complexity but yield good statistical efficiency. The paper also presents various properties of parameter estimators for the errors-in-variables problem, and a few conjectures are included, as well as some perspectives and experiences by the authors.