Recent advances in pre-training of word embeddings and language models leverage large amounts of unlabelled texts and self-supervised learning to learn distributed representations that have significantly improved the performance of deep learning models on a large variety of natural language processing tasks. Similarly, multilingual variants of these models have been developed from web-crawled multilingual resources like Wikipedia and Common crawl. However, there are some drawbacks to building these multilingual representation models. First, the models only include few low-resource languages in the training corpus, and additionally, the texts of these languages are often noisy or of low quality texts. Second, their performance on downstream NLP tasks is difficult to evaluate because of the absence of labelled datasets, therefore, they are typically only evaluated on English and other high-resource languages. In this dissertation, we focus on languages spoken in Sub-Saharan Africa where all the indigenous languages in this region can be regarded as low-resourced in terms of the availability of labelled data for NLP tasks and unlabelled data found on the web. We analyse the noise in the publicly available corpora, and curate a high-quality corpus, demonstrating that the quality of semantic representations learned in word embeddings does not only depend on the amount of data but on the quality of pre-training data. We demonstrate empirically the limitations of word embeddings, and the opportunities the multilingual pre-trained language model (PLM) offers especially for languages unseen during pre-training and low-resource scenarios. We further study how to adapt and specialize multilingual PLMs to unseen African languages using a small amount of monolingual texts. To address the under-representation of the African languages in NLP research, we developed large scale human-annotated labelled datasets for 21 African languages in two impactful NLP tasks: named entity recognition and machine translation. We conduct an extensive empirical evaluation using state-of-the-art methods across supervised, weakly-supervised, and transfer learning settings. In order to advance the progress of NLP for African languages, future work should focus on expanding benchmark datasets for African languages in other important NLP tasks like part of speech tagging, sentiment analysis, hate speech detection, and question answering. Another direction is to focus on development of Africa-centric PLMs. Lastly, research on speech that involves developing corpora and techniques that require zero or few paired speech-text data would be very essential for the survival of many under-resourced African languages.