Cross-domain few-shot learning (CDFSL) addresses learning problems where knowledge needs to be transferred from one or more source domains into an instance-scarce target domain with an explicitly different distribution. Recently published CDFSL methods generally construct a universal model that combines knowledge of multiple source domains into one feature extractor. This enables efficient inference but necessitates re-computation of the extractor whenever a new source domain is added. Some of these methods are also incompatible with heterogeneous source domain extractor architectures. The first part of this thesis proposes feature extractor stacking (FES), a new CDFSL method for combining information from a collection of extractors, that can utilise heterogeneous pretrained extractors out of the box and does not maintain a universal model that needs to be re-computed when its extractor collection is updated. We present the basic FES algorithm, which is inspired by the classic stacked generalisation approach, and also introduce two variants: convolutional FES (ConFES) and regularised FES (ReFES). Given a target-domain task, these algorithms fine-tune each extractor independently, use cross-validation to extract training data for stacked generalisation from the support set, and learn a simple linear stacking classifier from this data. We evaluate our FES methods on the well-known Meta-Dataset benchmark, targeting image classification with convolutional neural networks, and show that they can achieve state-of-the-art performance. The second part of this thesis proposes an efficient semi-supervised learning method that applies self-training to the classification head only and show that it can yield very consistent improvements in average performance in the Meta-Dataset benchmark for cross-domain few-shot learning when applied with FES and other contemporary methods utilising centroid-based classification. The third part of this thesis proposes a bidirectional snapshot selection strategy for FES, leveraging its cross-validation process and the ordered nature of its snapshots, and demonstrates that a 95% snapshot reduction can be achieved while retaining the same level of accuracy.