Signal coding or compression has played a significant role in the success of digital communications and multimedia. The use of signal coding pervades many aspects of our digital lifestyle-a lifestyle that has seen widespread demand for applications like third generation mobile telephony, portable music players, Internet-based video conferencing, digital television, etc. The issues that arise, when dealing with the transmission and storage of digital media, are the limited bandwidth of communication channels, the limited capacity of storage devices, and the limited processing ability of the encoding and decoding devices. The aim of signal coding is therefore to represent digital media, such as speech, music, images, and video, as efficiently as possible. Coding efficiency encompasses rate-distortion (for lossy coding), computational complexity, and static memory requirements. The fundamental operation in lossy signal coding is quantisation. Its rate-distortion efficiency is influenced by the properties of the signal source, such as statistical dependencies and its probability density function. Vector quantisers are known to theoretically achieve the lowest distortion, at a given rate and dimension, of any quantisation scheme, though their computational complexity and memory requirements grow exponentially with rate and dimension. Structurally constrained vector quantisers, such as product code vector quantisers, alleviate these complexity issues, though this is achieved at the cost of degraded rate-distortion performance. Block quantisers or transform coders, which are a special case of product code vector quantisation, possess both low computational and memory requirements, as well as the ability to scale to any bitrate, which is termed as bitrate scalability. However, the prerequisite for optimal block quantisation, namely a purely Gaussian data source with uniform correlation, is rarely ever met with real-world signals. The Gaussian mixture model-based block quantiser, which was originally developed for line spectral frequency (LSF) quantisation for speech coding, overcomes these problems of source mismatch and non-stationarity by estimating the source using a GMM. The split vector quantiser, which was also successfully applied to LSF quantisation in the speech coding literature, is a product code vector quantiser that overcomes the complexity problem of unconstrained vector quantisers, by partitioning vectors into sub-vectors and quantising each one independently. The complexity can be significant reduced via more vector splitting, though this inevitably leads to an accompanying degradation in the rate-distortion efficiency. This is because the structural constraint of vector splitting causes losses in several properties of vector quantisers, which are termed as 'advantages'. This dissertation makes several contributions to the area of block and vector quantisation, more specifically to the GMM-based block quantiser and split vector quantiser, which aim to improve their rate-distortion and computational efficiency. These new quantisation schemes are evaluated and compared with existing and popular schemes in the areas of lossy image coding, LSF quantisation in narrowband speech coding, LSF and immittance spectral pair (ISP) quantisation in wideband speech coding, and Mel frequency-warped cepstral coefficient (MFCC) quantisation in distributed speech recognition. These contributions are summarised below. A novel technique for encoding fractional bits in a fixed-rate 0MM-based block quantiser scheme is presented. In the 0MM-based block quantiser, fractional bitrates are often assigned to each of the cluster block quantisers. This new encoding technique leads to better utilisation of the bit budget by allowing the use of, and providing for the encoding of, quantiser levels in a fixed-rate framework. The algorithm is based on a generalised positional number system and has a low complexity. A lower complexity 0MM-based block quantiser, that replaces the KLT with the discrete cosine transform (DOT), is proposed for image coding. Due to its source independent nature and amenability to efficient implementation, the DOT allows a fast 0MM-based block quantiser to be realised that achieves comparable rate-distortion performance as the KLT-based scheme in the block quantisation of images. Transform image coding often suffers from block artifacts at relatively low bitrates. We propose a scheme that minimises the block artifacts of block quantisation by pre-processing the image using the discrete wavelet transform, extracting vectors via a tree structure that exploits spatial self-similarity, and quantising these vectors using the 0MM-based block quantiser. Visual examination shows that block artifacts are considerably reduced by the wavelet pre-processing step. The multi-frame 0MM-based block quantiser is a modified scheme that exploits memory across successive frames or vectors. Its main advantages over the memoryless scheme in the application of LSF and ISP quantisation, are better rate-distortion and computational efficiency, through the exploitation of correlation across multiple frames and mean squared error selection criterion, respectively. The multi-frame 0MM-based block quantiser is also evaluated for the quantisation of MFCC feature vectors for distributed speech recognition and is shown to be superior to all quantisation schemes considered. A new product code vector quantiser, called the switched split vector quantiser (SSVQ), is proposed for speech LSF and ISP quantisation. SSVQ is a hybrid scheme, combining a switch vector quantiser with several split vector quantisers. It aims to overcome the losses of rate-distortion efficiency in split vector quantisers, by exploiting full vector dependencies before the vector splitting. It is shown that the SSVQ alleviates the losses in two of the three vector quantiser 'advantages'. The SSVQ also has a remarkably low computational complexity, though this is achieved at the cost of an increase in memory requirements.