Conversational AI is one of the most active research areas in AI, and it has gained more attention from academia as well as industry. Given recent advancements in several conversational AI systems in addition to the availability of several datasets, the aim of this study is to explore the landscape of Arabic text-based conversational AI systems. In this work, we provide a thorough review of recent Arabic conversational AI systems. We group them into three categories based on their functionality: (1) question-answering (QA) systems, (2) task-oriented dialogue systems (DS), and (3) chatbots. Furthermore, we describe the common datasets used in building and evaluating conversational AI systems in Arabic. Few surveys have targeted the conversational AI field for the Arabic language, and we aim to cover this gap with this study. Our contribution focuses on reviewing and analyzing the literature in the field and highlighting future research directions towards human-like conversational AI systems in Arabic.