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The presentation will outline two examples of the use of measurement error models in small area estimation. The first one is methodological work when measurement error is introduced in a continuous outcome by reporting only the band in which the corresponding measurement belongs to- hence- resulting in interval censored data. This is a typical approach when collecting income data and interest is in (a) reducing the survey burden and (b) increasing the confidentiality of the data. However, this approach data collection also reduces the information available which has implications for small area estimation. We present methodology that reverses the measurement error process by reconstructing the distribution of the continuous outcome and uses this for small area estimation. The method is illustrated in an application for estimating income deprivation and inequality for small areas. The second part of the presentation is devoted to the case when model covariates are measured with error for example, because they are derived from another, typically, larger survey. In this case we will consider area level models and describe an application of the Ybarra and Lohr (2008) approach for estimating discontinuities in national surveys. Finally, a summary of current work on the topic will be presented.