In this thesis, we study two approaches to multi-stream sequential change detection, both based on the likelihood ratio test. In statistical sequential change detection, the problem is to detect a change as quickly as possible, restricted by a specified rate of false alarms. Since changes in high-dimensional data streams often only affect a small subset of the individual streams, the mixture approach incorporates an assumption about the sparsity of a change. The projection approach, on the other hand, first reduces the dimension of the multivariate data stream, then detects changes in the transformed stream. The existing procedures within each approach only consider changes occuring in the mean of independent, constant-variance data streams. We extend each procedure by deriving statistics that can detect an abrupt change in the covariance matrix, the mean or both. Our projection procedure handles general covariance matrices, whereas the mixture procedure assumes that the covariance matrix is diagonal. The dimension reduction techniques we consider in combination with our projection procedure are Gaussian random projections, principal component analysis and stationary subspace analysis. Through simulation experiments with a 100-dimensional data stream, we investigate which methods that yield the quickest detection in different change scenarios. The change scenarios include changes in mean, variance and correlations, where we vary the size and sparsity of a change. We also discuss in what ways the methods are limited by an increasing number of streams. Most notably, our results show that changes in a general covariance matrix can be detected almost instantly by using the least varying principal components in the projection procedure, for almost any sparsity of the change. In its current form, stationary subspace analysis proved to be unfit for sequential analysis. If the streams are independent, the mixture procedure for a change in the variances and/or mean also exhibits promising performance for changes in the variance.