Interest in manifold learning for representing the topology of large, high dimensional nonlinear data sets in lower, but still meaningful dimensions for visualization and analysis has grown rapidly over the past decade, including analysis of hyperspectral remote sensing data. The high spectral resolution and the typically continuous bands of hyperspectral image (HSI) data enable discrimination between spectrally similar targets of interest, provide capability to estimate within pixel abundances of constituents, and allow direct exploitation of absorption features in predictive models. Although hyperspectral data are typically modeled assuming that the data originate from linear stochastic processes, nonlinearities are often exhibited in the data due to the effects of multipath scattering, variations in sun-canopy-sensor geometry, The machine learning community has demonstrated the potential of manifold based approaches for nonlinear dimensionality reduction and modeling of nonlinear structure. nonhomogeneous composition of pixels, and attenuating properties of media. Because of the dense spectral sampling of HSI data, the associated spectral information in many adjacent bands is highly correlated, resulting in much lower intrinsic dimensions spanned by the data. Increased availability of HSI and greater access to advanced computing have motivated development of specialized methods for exploitation of nonlinear characteristics of these data. Theoretical contributions and applications of manifold learning have progressed in tandem, with new results providing capability for data analysis, and applications highlighting limitations in existing methods. The machine learning community has demonstrated the potential of manifold based approaches for nonlinear dimensionality reduction and modeling of nonlinear structure. For HSI, the enormous size of the data sets and spatial clustering of classes on the image grid provide both challenges and opportunities to extend manifold learning methods. The potential value of manifold learning for HSI analysis has been demonstrated for remote sensing applications including feature extraction, segmentation, classification, anomaly detection, and spectral unmixing with recent approaches exploiting inter-band correlation and local spatial homogeneity. Challenges encountered in analyzing data sets have inspired recent advances in manifold learning methods. This presentation provides an overview of manifold learning methods recently developed for classification and unmixing of hyperspectral image data, including intelligent selection of landmarks to represent the manifold, spatial-spectral methods, and approaches that jointly exploit local and global geometry.