We consider different options for the search for possible variations of the fundamental constants. We give a brief overview of the results obtained with several methods. We discuss their advantages and disadvantages with respect to simultaneous variations of all constants in both time and space in the range 108–1010 years. We also suggest a few possibilities for the laboratory search. Particularly, we propose some experiments with the hyperfine structure of hydrogen, deuterium, and ytterbium–171 and of some atoms with a small magnetic moment. Other suggestions are for some measurements of the fine structure associated with the ground state. Special attention is paid to the interpretation of the hfs measurements in terms of variations of the fundamental constants. PACS No.: 31.30G