Extreme learning machines (ELMs) have proven to be efficient and effective learning mechanisms for pattern classification and regression. However, ELMs are primarily applied to supervised learning problems. Only a few existing research papers have used ELMs to explore unlabeled data. In this paper, we extend ELMs for both semi-supervised and unsupervised tasks based on the manifold regularization, thus greatly expanding the applicability of ELMs. The key advantages of the proposed algorithms are as follows: 1) both the semi-supervised ELM (SS-ELM) and the unsupervised ELM (US-ELM) exhibit learning capability and computational efficiency of ELMs; 2) both algorithms naturally handle multiclass classification or multicluster clustering; and 3) both algorithms are inductive and can handle unseen data at test time directly. Moreover, it is shown in this paper that all the supervised, semi-supervised, and unsupervised ELMs can actually be put into a unified framework. This provides new perspectives for understanding the mechanism of random feature mapping, which is the key concept in ELM theory. Empirical study on a wide range of data sets demonstrates that the proposed algorithms are competitive with the state-of-the-art semi-supervised or unsupervised learning algorithms in terms of accuracy and efficiency.