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Despite wide adoption, measure selection is often decoupled from estimator assumptions, failure modes, and safe inferential claims. This survey provides a practical decision framework for four foundational measures - Entropy, KL divergence/cross-entropy, Mutual Information, and Transfer Entropy - organized around three prescriptive questions for each: (i) what question does the measure answer and in which AI context; (ii) which estimator is appropriate for the data type and dimensionality; and (iii) what is the most dangerous misuse. 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This survey provides a practical decision framework for four foundational measures - Entropy, KL divergence/cross-entropy, Mutual Information, and Transfer Entropy - organized around three prescriptive questions for each: (i) what question does the measure answer and in which AI context; (ii) which estimator is appropriate for the data type and dimensionality; and (iii) what is the most dangerous misuse. 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