The analysis of compositional data using the log-ratio approach is based on ratios between the compositional parts. Zeros in the parts thus cause severe difficulties for the analysis. Log-ratio transformations represent the compositional information into new coordinates. Outliers within these coordinates may be detected, however it remains unclear which particular parts of the composition led to the deviating ratios in question. To address this issue, the thesis presents four exploratory tools for identifying cellwise outliers in compositional data sets with structural zeros. In order to deal with structural zeros the proposed methods use robust imputation methods or split the data into subcompositions determined by their zero patterns. Ratios between parts are analyzed using an isometric log-ratio transformation or by observing pairwise log-ratios. Combining the results from robust regression analysis and robust distance calculations the approaches deduce row- and cellwise outliers within the original sample space. All four methods are applied on the household expenditure data from Albania and then compared. A close-to-reality simulation study is conducted to assess the performance of the different outlier detection algorithms.