Alphaviruses can replicate in arthropods and in many vertebrate species including humankind, but only in vertebrate cells do infections with these viruses result in a strong inhibition of host translation and transcription. Translation shutoff by alphaviruses is a multifactorial process that involves both host- and virus-induced mechanisms, and some of them are not completely understood. Alphavirus genomes contain cis-acting elements (RNA structures and dinucleotide composition) and encode protein activities that promote the translational and transcriptional resistance to type I IFN-induced antiviral effectors. Among them, IFIT1, ZAP and PKR have played a relevant role in alphavirus evolution, since they have promoted the emergence of multiple viral evasion mechanisms at the translational level. In this review, we will discuss how the adaptations of alphaviruses to vertebrate hosts likely involved the acquisition of new features in viral mRNAs and proteins to overcome the effect of type I IFN.