Arabic dialects also called colloquial Arabic or vernaculars are spoken varieties of Standard Arabic. These dialects have mixed form with many variations due to the influence of ancient local tongues and other languages like European ones. Many of these dialects are mutually incomprehensible. Arabic dialects were not written until recently and were used only in a speech form. Nowadays, with the advent of the internet and mobile telephony technologies, these dialects are increasingly used in a written form. Indeed, this kind of communication brought everyday conversations to a written format. This allows Arab people to use their dialects, which are their actual native languages for expressing their opinion on social media, for chatting, texting, etc. This growing use opens new research direction for Arabic natural language processing (NLP). We focus, in this paper, on machine translation in the context of Arabic dialects. We provide a survey of recent research in this area. We report for each study a detailed description of the adopted approach and we give its most relevant contribution.