The inhibition of beta-secretase has become a very promising approach to control the onset and progression of Alzheimer's disease due to its involvement in the generation of amyloid plaques. The main goal of the many drug discovery projects targeting this enzyme is the identification of highly specific, non-peptidic compounds with low molecular weight, characteristics that are desirable for drug leads with low toxicity that have to transverse the blood brain barrier. We describe the main approaches used in the discovery of novel inhibitors, including substrate specificity, target structure based design, and high throughput screening (HTS), both in vitro and in silico. We place special emphasis in the receptor based design and in silico HTS, two strategies that make wide use of computer assisted tools. To exemplify the usefulness and versatility of computer tools in this endeavor we use the computer generated 'enzyme's binding site cast' to rationalize qualitatively some salient structural features of known beta-secretase second generation inhibitors, and for guiding the review of many of the ligands whose complexes with the enzyme have been studied by X-ray crystallography. We discuss the use made by other authors of molecular modelling for the understanding of the very special characteristics of ligand binding to beta-secretase and for the design of new inhibitors. Finally, we review the quest for non-peptidic inhibitors that has led to the use of HTS in vitro and in silico. The screening of extensive libraries resulted in a few low affinity compounds that do not fit into the key S1/S1' pockets, indicating that this is not an easy target to block.