In recent years, Natural Language Processing has improved significantly, but most developments favor high-resource languages. Due to the absence of annotated corpora, lexical databases, and computational tools many languages are under-resourced. Morphosyntactic analysis is a fundamental component of several NLP tasks, including part-of-speech tagging, syntactic parsing, and machine translation. It focuses on understanding words forms and sentence structure in a language. The under-resources languages have limited linguistic resources and contain complex morphological structures which makes the development of computational approaches for morphosyntactic analysis challenging. This study reviews different computational methods used for morphosyntactic analysis in under-resourced languages. 19 studies were reviewed to examine the technique used, research areas and performance trends in the literature. The results show that the percentage of neural network-based is about 42% of the analyzed literature, then statistical ML methods 32% and the rule-based approaches 26%. In Performance comparison the neural network models (82%) achieve higher accuracy compared to statistical models (75%) and rule-based models (70%). Also, it shows that the morphological processing and language resource development is the most investigated research areas. These developments and performance of the models are affected by limited annotated datasets and linguistic diversity. The results show the need for better linguistic resources and hybrid computational approaches for morphosyntactic analysis in under-resourced languages. These can help guide future research to develop better NLP tools for these languages.