You could look at this book, or this handout, which will give you some references. From a linguistic perspective, translation is both extremely complex and extremely simple. I think that there does exist "out there" a notion is that there is an abstract language-independent mental state connected to any language utterance ("the meaning"), and that to translate from English to Logoori, we just have to figure out the rules for getting from actual utterances of Logoori to that Platonic inner form, then from that inner form to its "equivalent" in English. Success would be defined as the case we can reliably devise a system that faithfully identifies those real-word states of affairs associated with utterances in the minds of English speakers and Logoori systems.
A first step would be to somehow identify those mental states of speakers of only one language – what mental state arises when a Logoori speaker says maa ryaanga rinwiihizi amavaru? A very crude translation into English would be "The aardvark will make the ants drink". However, there are nearly a dozen future forms in this language, defined by subtle nuances (e.g. whether the event is expected to happen immediately, vs. in 2-3 days, or some further time on the future). Not only do speakers not agree with each other as to the time boundaries of this particular tense, they don't consistently agree with themselves, that is, the mental state that arises is not trivially replicable given just re-presentation of the linguistic form. It is also highly influenced by whatever real-world facts are most prominent in the speaker's mind at the moment that they receive and interpret the utterance. It is possible, however, to devise a general rule that is relatively simple which does describe a decent percentage of the mental states of speakers of the language (as a statistical abstraction) when they use this verb form – it will happen about 2-3 days in the future, as you push the margins to 3.5 or 4 days there is a decrease in speaker agreement.
The nouns ryaanga 'aardvark' and amavaru 'ants' cause highly variable mental states across speakers. I suspect that 'aardvark' creates similar variable mental states among US English speakers, since we never encounter aardvarks in the wild and most people may not now know that "A is for aadvark", or remember what one looks like from 1st grade. Some words are sufficiently obscure that the referent is not well known. The word amavaru refers to a a specific class of ants – there are dozens of ant names in the language, and most people have only a loose understanding of exactly which ants that refers to. The best guess is that it refers to ants of the genus Dorylus.
In light of these considerations, an attempt to capture a precise mental state of all speakers of a language is hopeless, but there is hope if one accepts the goal as being devising a mapping that "best" identifies the mental states of most speakers in most circumstances. That means "2-3 days future", "wild animal that eats ants" and "black big-headed ant in huge armies".
One might then translate the sentence into English as "The wild animal that eats ants will, within about 2-3 days, cause the black big-headed ants in huge armies to drink" (there are some subtle nuances about "cause to drink" that we can gloss over). The translation so produced is really terrible – nobody would ever say that (leaving aside the situational strangeness of the sentence). In translating between Logoori and English, one will have to lose additional information, perhaps calling the ants "army ants" (but we don't have army ants, and in an attempt to devise the best actual mental state of the most English speakers, we need to just translate the inset name to "ants"), and ignoring the nuances of the various future forms. We can however gain some increase in accuracy of identification by using the word 'aardvark' (if indeed people have a mental referent for aardvark).
The main linguistic question starts with asking what it means to "translate". Linguistic does not dictate word meaning, so we cannot tell you what it means to "translate", but if you have a theory of what it means to "translate", then linguistics might offer analytic insights. Linguists do not agree on the status of the supposed invariant "inner language of thought" – some people believe, some disbelieve.
