By searching for new copper-based metallics, interest in various copper complexes has increased. Copper complexes appear as auspicious potential diagnostics and medicaments in the treatment of cancer. Copper is a microbiogenic element and any biogenic element that escapes its metabolic tracks can affect the organism in a harmful way, therefore copper complexes can serve as cytotoxic compounds. The bachelor thesis deals with an overview of copper complexes studies with the most fitting ligands such as phenanthroline, bipyridine, benzimidazole and others. Moreover, it involves compounds suitable for diagnosis by PET such as the 64Cu isotope. The aim of my bachelors was to study and gather Cu complexes, which were either examined on different cancer cell lines or got into the phase I , alternatively, to the phase II of the clinical study.