Automated analysis of temporal data is a task of utmost importance for intelligent machines. For example, ubiquitous computing systems need to understand the intention of humans from the stream of sensory information, and health-care monitoring systems can assist patients and doctors by providing automatically annotated daily health reports. We present a set of extensions of switching linear dynamic systems (SLDSs) which provide the ability to capture the higher-order temporal structures within data and to produce more accurate results for the tasks such as labeling and estimation of global variations within data. The presented models are formulated within a dynamic Bayesian network formulation along with the inference and learning methods thereof. First, segmental SLDSs (S-SLDSs) produce superior labeling results by capturing the descriptive duration patterns within each LDS segment. The encoded duration models describe data more descriptively and allow us to avoid the severe problem of over-segmented labels, which leads to superior accuracy. Second, parametric SLDSs (P-SLDSs) allows us to encode the temporal data with global variations. In particular, we have identified two types of global systematic variations : temporal and spatial variations. The P-SLDS model assumes that there is an underlying canonical model which is globally transformed in time and space by the two associated global parameters respectively. Third, we present hierarchical SLDSs (H-SLDSs), a generalization of standard SLDSs with hierarchic Markov chains. H-SLDSs are able to encode temporal data which exhibits hierarchic structure where the underlying low-level temporal patterns repeatedly appear among different higher-level contexts. The developed SLDS extensions have been applied to two real-world problems. The first problem is to automatically decode the dance messages of honey bee dances where the goal is to correctly segment the dance sequences into different regimes and parse the messages about the location of food sources embedded in the data. The second problem is to analyze wearable exercise data where we aim to provide an automatically generated exercise record at multiple temporal and semantic resolutions. It is demonstrated that the H-SLDS model with multiple layers can be learned from data, and can be successfully applied to interpret the exercise data at multiple granularities.