Despite recent advances in natural language processing, there is still a gap in state-of-the-art methods to address problems related to low-resource and morphologically-rich languages. These methods are data-hungry, and due to the scarcity of training data for low-resource and morphologically-rich languages, developing NLP tools for them is a challenging task. Approaches for forming cross-lingual embeddings and transferring knowledge from a rich- to a low-resource language have emerged to overcome the lack of training data. Although in recent years we have seen major improvements in cross-lingual methods, these methods still have some limitations that have not been addressed properly. An important problem is the out-of-vocabulary word (OOV) problem, i.e., words that occur in a document being processed, but that the model did not observe during training. The OOV problem is more significant in the case of low-resource languages, since there is relatively little training data available for them, and also in the case of morphologically-rich languages, since it is very likely that we do not observe a considerable number of their word forms in the training data. Approaches to learning sub-word embeddings have been proposed to address the OOV problem in monolingual models, but most prior work has not considered sub-word embeddings in cross-lingual models. The hypothesis of this thesis is that it is possible to leverage sub-word information to overcome the OOV problem in low-resource and morphologically-rich languages. This thesis presents a novel bilingual lexicon induction task to demonstrate the effectiveness of sub-word information in the cross-lingual space and how it can be employed to overcome the OOV problem. Moreover, this thesis presents a novel cross-lingual word representation method that incorporates sub-word information during the training process to learn a better cross-lingual shared space and also better represent OOVs in the shared space. This method is particularly suitable for low-resource scenarios and this claim is proven through a series of experiments on bilingual lexicon induction, monolingual word similarity, and a downstream task, document classification. More specifically, it is shown that this method is suitable for low-resource languages by conducting bilingual lexicon induction on twelve low-resource and morphologically-rich languages.