Advances in the area of ubiquitous, pervasive and wearable computing have resulted in the development of low band-width, data rich environmental and body sensor networks, providing a reliable and non-intrusive methodology for capturing activity data from humans and the environments they inhabit. Assistive technologies that promote independent living amongst elderly and individuals with cognitive impairment are a major motivating factor for sensor-based activity recognition systems. However, the process of discerning relevant activity information from these sensor streams such as accelerometers is a non-trivial task and is an on-going research area. The difficulty stems from factors such as spatio-temporal variations in movement patterns induced by different individuals and contexts, sparse occurrence of relevant activity gestures in a continuous stream of irrelevant movements and the lack of real-world data for training learning algorithms. This work addresses these challenges in the context of wearable accelerometer-based simple activity and gesture recognition. The proposed computational framework utilizes discriminative classifiers for learning the spatio-temporal variations in movement patterns and demonstrates its effectiveness through a real-time simple activity recognition system and short duration, non- repetitive activity gesture recognition. Furthermore, it proposes adaptive discriminative threshold models trained only on relevant activity gestures for filtering irrelevant movement patterns in a continuous stream. These models are integrated into a gesture spotting network for detecting activity gestures involved in complex activities of daily living. The framework addresses the lack of real world data for training, by using auxiliary, yet related data samples for training in a transfer learning setting. Finally the problem of predicting activity tasks involved in the execution of a complex activity of daily living is described and a solution based on hierarchical Markov models is discussed and evaluated.