An essential characteristic of chemical compounds is their biological activity since its presence can become the basis for the use of the substance for therapeutic purposes, or, on the contrary, limit the possibilities of its practical application due to the manifestation of side action and toxic effects. Computer assessment of the biological activity spectra makes it possible to determine the most promising directions for the study of the pharmacological action of particular substances, and to filter out potentially dangerous molecules at the early stages of research. For more than 25 years, we have been developing and improving the computer program PASS (Prediction of Activity Spectra for Substances), designed to predict the biological activity spectrum of substance based on the structural formula of its molecules. The prediction is carried out by the analysis of structure-activity relationships for the training set, which currently contains information on structures and known biological activities for more than one million molecules. The structure of the organic compound is represented in PASS using Multilevel Neighborhoods of Atoms descriptors; the activity prediction for new compounds is performed by the naive Bayes classifier and the structure-activity relationships determined by the analysis of the training set. We have created and improved both local versions of the PASS program and freely available web resources based on PASS (http://www.way2drug.com). They predict several thousand biological activities (pharmacological effects, molecular mechanisms of action, specific toxicity and adverse effects, interaction with the unwanted targets, metabolism and action on molecular transport), cytotoxicity for tumor and non-tumor cell lines, carcinogenicity, induced changes of gene expression profiles, metabolic sites of the major enzymes of the first and second phases of xenobiotics biotransformation, and belonging to substrates and/or metabolites of metabolic enzymes. The web resource Way2Drug is used by over 18,000 researchers from more than 90 countries around the world, which allowed them to obtain over 600,000 predictions and publish about 500 papers describing the obtained results. The analysis of the published works shows that in some cases the interpretation of the prediction results presented by the authors of these publications requires an adjustment. In this work, we provide the theoretical basis and consider, on particular examples, the opportunities and limitations of computer-aided prediction of biological activity spectra.