So I have looked up the word 'eulogy' in a number of dictionaries.
In the Cambridge Advanced Learner's Dictionary, the definition states: "a speech, piece of writing, poem, etc. containing great praise, especially for someone who recently died or stopped working."
They also offer an explanation for the verb 'eulogize', as follows: "to praise someone or something in a speech or piece of writing."
Critics everywhere have eulogized her new novel.
They eulogized over the breathtaking views.
Dictionary.com offers a number of definitions and historical background too, which is enlightening. Their definition from Random House Dictionary goes like this:
1. "a speech or writing in praise of a person or thing, esp. a set oration in honor of a deceased person."
2. "high praise or commendation."
The American Hermitage Dictionary of the English Language Fourth Edition is similar in its definition: