We review the state of the art in DNA micro array image compression. First, we describe the most relevant approaches published in the literature and classify them according to the stage of the typical image compression process where each approach makes its contribution. We then summarize the compression results reported for these specific-specific image compression schemes. In a set of experiments conducted for this paper, we obtain results for several popular image coding techniques, including the most recent coding standards. Prediction-based schemes CALIC and JPEG-LS, and JPEG2000 using zero wavelet decomposition levels are the best performing standard compressors, but are all outperformed by the best micro array-specific technique, Battiato's CNN-based scheme.