In recent years data streams became a ubiquitous source of information, and thus stream mining emerged as a new field in database research. Due to the inherently dynamic nature of data streams, stream mining algorithms benefit from being adaptive to changes in the properties of a data stream. In addition, when stream mining is done in a dynamic environment like a data stream management system or a sensor network, stream mining algorithms also profit from being adaptive to the changing conditions in this environment. This work investigates two kinds of adaptivity in data stream mining. First, a model for quality-driven resource adaptive stream mining is developed. The model is applied to stream mining algorithms so they efficiently utilize available resources to achieve mining results of the highest quality possible. Every stream mining algorithm is unique in its parameters, quality measures, and resource consumption patterns. We generalize these characteristics and develop a model that captures the interactions and correlations between variables involved in the stream mining process. We then express resource adaptive stream mining as a multiobjective optimization problem and use its solution to tune the input parameters of stream mining algorithms, which results in high quality mining and optimal resource utilization. The second topic investigated in this work is feature adaptive stream mining, which is concerned with adjusting the focus of the mining process to interesting features detected in the data stream. This research is motivated by the need to efficiently detect environmental phenomena from sensor data streams. We propose methods to detect and predict heterogeneous outlier regions, which represent areas of environmental phenomena of different intensities. With the help of predictions about the location and size of outlier regions, the sampling rate of individual sensors is adapted such that sensors in the vicinity of environmental phenomena obtain new measurements more frequently than other sensors in the network to allow for a precise and timely region tracking. The research in this work enhances the state-of-the-art in data stream mining as it makes stream mining algorithms more flexible to adapt to changes in the data stream and the mining environment.