Motivated by the variability in hyperspectral images due to illumination and the difficulty in acquiring labelled data, this thesis proposes different approaches for learning illumination invariant feature representations and classification models for hyperspectral data captured outdoors, under natural sunlight. The approaches integrate domain knowledge into learning algorithms and hence does not rely on a priori knowledge of atmospheric parameters, additional sensors or large amounts of labelled training data. Hyperspectral sensors record rich semantic information from a scene, making them useful for robotics or remote sensing applications where perception systems are used to gain an understanding of the scene. Images recorded by hyperspectral sensors can, however, be affected to varying degrees by intrinsic factors relating to the sensor itself (keystone, smile, noise, particularly at the limits of the sensed spectral range) but also by extrinsic factors such as the way the scene is illuminated. The appearance of the scene in the image is tied to the incident illumination which is dependent on variables such as the position of the sun, geometry of the surface and the prevailing atmospheric conditions. Effects like shadows can make the appearance and spectral characteristics of identical materials to be significantly different. This degrades the performance of high-level algorithms that use hyperspectral data, such as those that do classification and clustering. If sufficient training data is available, learning algorithms such as neural networks can capture variability in the scene appearance and be trained to compensate for it. Learning algorithms are advantageous for this task because they do not require a priori knowledge of the prevailing atmospheric conditions or data from additional sensors. Labelling of hyperspectral data is, however, difficult and time-consuming, so acquiring enough labelled samples for the learning algorithm to adequately capture the scene appearance is challenging. Hence, there is a need for the development of techniques that are invariant to the effects of illumination that do not require large amounts of labelled data. In this thesis, an approach to learning a representation of hyperspectral data that is invariant to the effects of illumination is proposed. This approach combines a physics-based model of the illumination process with an unsupervised deep learning algorithm, and thus requires no labelled data. Datasets that vary both temporally and spatially are used to compare the proposed approach to other similar state-of-the-art techniques. The results show that the learnt representation is more invariant to shadows in the image and to variations in brightness due to changes in the scene topography or position of the sun in the sky. The results also show that a supervised classifier can predict class labels more accurately and more consistently across time when images are represented using the proposed method. Additionally, this thesis proposes methods to train supervised classification models to be more robust to variations in illumination where only limited amounts of labelled data are available. The transfer of knowledge from well-labelled datasets to poorly labelled datasets for classification is investigated. A method is also proposed for enabling small amounts of labelled samples to capture the variability in spectra across the scene. These samples are then used to train a classifier to be robust to the variability in the data caused by variations in illumination. The results show that these approaches make convolutional neural network classifiers more robust and achieve better performance when there is limited labelled training data. A case study is presented where a pipeline is proposed that incorporates the methods proposed in this thesis for learning robust feature representations and classification models. A scene is clustered using no labelled data. The results show that the pipeline groups the data into clusters that are consistent with the spatial distribution of the classes in the scene as determined from ground truth.