Microscopic images are frequently used in medicine and molecular biology. Many interesting image processing problems arise after the initial data acquisition step, since image modalities are manifold. In this thesis, we developed several algorithms in order to handle the critical pipeline of microscopic image storage/ compression and analysis/classification more efficiently. The first step in our processing pipeline is image compression. Microscopic images are large in size (e.g. 100K-by-100K pixels), therefore finding efficient ways of compressing such data is necessary for efficient transmission, storage and evaluation. We propose an image compression scheme that uses the color content of a given image, by applying a block-adaptive color transform. Microscopic images of tissues have a very specific color palette due to the staining process they undergo before data acquisition. The proposed color transform takes advantage of this fact and can be incorporated into widely-used compression algorithms such as JPEG and JPEG 2000 without creating any overhead at the receiver due to its DPCM-like structure. We obtained peak signal-to-noise ratio gains up to 0.5 dB when comparing our method with standard JPEG. The next step in our processing pipeline is image analysis. Microscopic image processing techniques can assist in making grading and diagnosis of images reproducible and by providing useful quantitative measures for computer-aided diagnosis. To this end, we developed several novel techniques for efficient feature extraction and classification of microscopic images. We use region co-difference matrices as inputs for the classifier, which have the main advantage of yielding multiplication-free computationally efficient algorithms. The merit of the co-difference framework for performing some important tasks in signal processing is discussed. We also introduce several methods that estimate underlying probability density functions from data. We use sparsity criteria in the Fourier domain to arrive at efficient estimates. The proposed methods can be used for classification in Bayesian frameworks. We evaluated the performance of our algorithms for two image classification problems: Discriminating between different grades of follicular lymphoma, a medical condition of the lymph system, as well as differentiating several cancer cell lines from each another. Classification accuracies over two large data sets (270 images for follicular lymphoma and 280 images for cancer cell lines) were above 98%.