The properties characterizing Sturmian words are considered forwords on multiliteral alphabets. Wesummarize various generalizations of Sturmian words tomultiliteral alphabets and enlarge the list of knownrelationships among these generalizations.We provide a new equivalent definition of rich wordsand make use of it in the study of generalizations of Sturmian words based on palindromes.We also collect many examples of infinite words to illustrate differences in thegeneralized definitions of Sturmian words.