The goal of this article is a general inspection of indexicals as a specific phenomenon of natural language on the one side, and a consideration of "semantization" of indexicals on the other side. The term "semantization" represents a criterion on the basis of which various approaches to relevant solutions are valuated: if, according to Frege´s view, all language expressions should express their senses, what kind of senses could be expressed in the case of indexicals? First, indexicals are explicated as a specific sort of language expressions. Second, how some contemporary philosophers deal with indexical puzzles is briefly propounded. It takes for granted that a comparison of various philosophers´ approaches makes their pro et contra clear. By that way the article can acquire a parameter of basic synopsis. In certain passages of the text, summaries of the issues dealt with are included. The article is divided into three parts, dividing idexicals into temporal, individual and spatial, and demonstratives. The second part of this article deals with individual and spatial indexicals. An additional problem is introduced in this way: do proper names refer through some fregean sense or do they not? The approaches of Russell, Kripke, Searle, Kaplan, Tichý, Materna and Quine are evaluated with reference to "semantization". In general the problem is again presented in a way that proper names can refer either directly or through some fregean sense. A problem arises as to the sort of that sense - if it is a bunch of descriptions or something else displayable.