The article discusses some of the burning or controversial questions that nowadays seem to affect the theory and practice of translation; questions such as freedom vs fidelity, overt vs covert translations, translatability vs untranslatability, translation equivalence vs adequacy, as well as translation units, translation invariable, etc. Some of these proposals and debates are as old as the activity of translation itself, and others have been raised after the establishment and consolidation of the field of Translation Studies as such. The authors tackle these highly topical issues, reviewing the different (and, at times, antagonistic) theoretical proposals and debates they have triggered off over the years.