The paper is a critical review of non-stochastic (referred here as deterministic) methods of calculation of effective elastic constants of single phase statistically homogeneous polycrystals. The methods are briefly described. They are compared and grouped according to their basic assumptions. Their degree of generality is discussed. The analysis of their compliance with formal requirements is provided. Moreover, the possible but unknown completions and generalizations of some methods are considered. For most methods, example calculations are carried out for a special case of quasi-isotropic aggregate with cubic crystal symmetry. To make the paper self-contained, well-known essentials of the problem of effective constants are included.