In addition to the information provided above, another obstacle to translating from one language to another occurs with idiomatic expressions and slang. These pose problems because they do not mean what the individual words mean literally, and these idioms often involve cultural history that a foreigner would not know. In fact, often these idiomatic expressions pose the most problems for foreign students who cannot make sense of what American students are saying when they use them. Some languages, such as French, have a plethora of idioms and slang that are difficult to translate. Also, in French there are many expressions that are composed of the verb faire, which means to do or to make; however, in English a person uses the verb to play [Je fais du foot] or to study [Je fais du francais] in such expressions. This occurs with German as well. For example, a German exchange student mostly fluent in English might still say "I make soccer."
Still another issue that arises from translating occurs between English and Italian when expressing one's feelings. The Italians have a myriad of words to express each nuance of feeling while English comes up short. So often Italians search for the word that will convey their feelings when they speak English.
As alluded to in the above response, poetry is extremely difficult to translate from one language to another as the rhythm of a poem can be marred, or even lost; the cultural meanings attached to phrases and the figurative meanings of words, etc. are often truly untranslatable.
Regarding the mention in the original question of technology as assistance in translation, it is effective in translating individual words and phrases, but many students have found themselves in trouble when they attempt the translation of entire passages.
Robert Frost famously said that poetry is “what gets lost in translation”. By this he meant that the nuances and aesthetic qualities of language are essential to poetry, and that those features are precisely what do not translate.
The difficulties of translation depend to a great degree on what you are translating and the nature of the two languages involved. A technical manual, which uses simple and precise language, will be much easier to translate than works of imaginative literature, which are steeped in literary traditions, allusions, and figurative language.
A major linguistic obstacle to translation is the problem of conceptual mapping. In simple cases, the relationship between signifier (a word) and concept (signified) is similar across numerous languages. The French "chat", Latin "feles", and English "cat" all are based on similar concepts of what constitutes the biological species. For other terms, the conceptual boundaries vary across languages. For example, the boundaries between colors vary from language to language. The Berber or Amazigh term "azegzaw" covers a range of shades that English separates into "blue" and "green".
A cultural obstacle has to do with terms referring to practices common in one culture but not in another, or where the significance of a term may not be immediately obvious in the target language. For example, the Latin verb "lucubrare" means to work by lamp or candlelight. In twenty-first century culture, we are accustomed to working by artificial light after dark, but this was something unusual in antiquity. Other ancient terms such as "miasma" in the sense of ritual pollution have no real modern English equivalent.