In numerous industrial applications, organizations wish to monitor time series data to better understand the past and make predictions for the future. To achieve this, appropriate analysis and modelling of time series data needs to be performed. However, it is common for time series to undergo abrupt structural changes, known as changepoints, which can cause major challenges during model fitting. Identifying changepoints is crucial to appropriately understand, analyze and model time series data in a wide range of applications including finance, genomics and countless others. In this thesis, we introduce new methodologies and frameworks for detecting changepoints in two scenarios; when there are multiple series to analyze simultaneously (multivariate setting) and when we receive time points sequentially and aim to detect changes as soon as possible (sequential setting). These methodologies provide novel and innovative ways to detect different types of changepoints in a wide range
of data structures. Firstly, we introduce a novel bivariate test statistic for detecting changes in mean and variance simultaneously in multivariate data. Our attention then turns to changes in covariance, specifically, we introduce a cost function and changepoint framework for identifying changes in subspace. Finally, we switch to the sequential changepoint setting and provide a framework for quickly identifying mean and variance changes in more complex data structures using forecast models. For all the methods we demonstrate their strong empirical performance in both simulated examples and industrial applications.