Modern Greek is normally written in the Greek alphabet. In informal online messages, however, Greek is often written using characters available on Latin-character keyboards, a form known as Greeklish. Originally used to bypass the lack of support for the Greek alphabet in older computers, Greeklish is now also used to avoid switching languages on multilingual keyboards, hide spelling mistakes, or as a form of slang. There is no consensus mapping, hence the same Greek word can be written in numerous different ways in Greeklish. Even native Greek speakers may struggle to understand (or be annoyed by) Greeklish, which requires paying careful attention to context to decipher. Greeklish may also be a problem for NLP models trained on Greek datasets written in the Greek alphabet. Experimenting with a range of statistical and deep learning models on both artificial and real-life Greeklish data, we find that: (i) prompting large language models (e.g., GPT-4) performs impressively well with few- or even zero-shot training, outperforming several fine-tuned encoder-decoder models; however (ii) a twenty years old statistical Greeklish transliteration model is still very competitive; and (iii) the problem is still far from having been solved; (iv) nevertheless, downstream Greek NLP systems that need to cope with Greeklish, such as moderation classifiers, can benefit significantly even with the current non-perfect transliteration systems. We make all our code, models, and data available and suggest future improvements, based on an analysis of our experimental results.