People nowadays are immersed in a wealth of text data, ranging from news articles, to social media, academic publications, advertisements, and economic reports. A grand challenge of data mining is to develop effective, scalable and weakly-supervised methods for extracting actionable structures and knowledge from massive text data. Without requiring extensive and corpus-specific human annotations, these methods will satisfy people's diverse applications and needs for comprehending and making good use of large-scale corpora. In this tutorial, we will introduce recent advances in text embeddings and their applications to a wide range of text mining tasks that facilitate multi-dimensional analysis of massive text corpora. Specifically, we first overview a set of recently developed unsupervised and weakly-supervised text embedding methods including state-of-the-art context-free embeddings and pre-trained language models that serve as the fundamentals for downstream tasks. We then present several embedding-driven text mining techniques that are weakly-supervised, domain-independent, language-agnostic, effective and scalable for mining and discovering structured knowledge, in the form of multi-dimensional topics and multi-faceted taxonomies, from large-scale text corpora. We finally show that the topics and taxonomies so discovered will naturally form a multi-dimensional TextCube structure, which greatly enhances text exploration and analysis for various important applications, including text classification, retrieval and summarization. We will demonstrate on the most recent real-world datasets (including political news articles as well as scientific publications related to the coronavirus) how multi-dimensional analysis of massive text corpora can be conducted with the introduced embedding-driven text mining techniques.