This paper presents a comprehensive review of Natural Language Processing (NLP) research on Armenian, a language that, despite its rich history and unique linguistic characteristics, is currently low-resource in the field of NLP. We critically synthesize and evaluate various studies in Armenian NLP, highlighting key advancements, challenges, and areas for improvement. A notable aspect of our work is the underlined lack of application of Large Language Models (LLMs) in Armenian NLP, signifying an area of potential exploration and development. Identifying and discussing these challenges and opportunities lays the groundwork for future research directions in Armenian NLP. The emphasis on Armenian also advocates for increased attention to low-resource languages in NLP research, stressing the importance of linguistic diversity and equity. To the best of our knowledge, this is the first paper providing such an extensive review of Armenian NLP, marking a significant contribution to the field.