Continuous change and development are essential aspects of evolving environments and applications, including, but not limited to, smart cities, military, medicine, nuclear reactors, self-driving cars, aviation, and aerospace. That is, the fundamental characteristics of such environments may evolve, and so cause dangerous consequences, e.g., putting people lives at stake, if no reaction is adopted. Therefore, learning systems need to apply intelligent algorithms to monitor evolvement in their environments and update themselves effectively. Further, we may experience fluctuations regarding the performance of learning algorithms due to the nature of incoming data as it continuously evolves. That is, the current efficient learning approach may become deprecated after a change in data or environment. Hence, the question 'how to have an efficient learning algorithm over time against evolving data?' has to be addressed. In this thesis, we have made two contributions to settle the challenges described above. In the machine learning literature, the phenomenon of (distributional) change in data is known as concept drift. Concept drift may shift decision boundaries, and cause a decline in accuracy. Learning algorithms, indeed, have to detect concept drift in evolving data streams and replace their predictive models accordingly. To address this challenge, adaptive learners have been devised which may utilize drift detection methods to locate the drift points in dynamic and changing data streams. A drift detection method able to discover the drift points quickly, with the lowest false positive and false negative rates, is preferred. False positive refers to incorrectly alarming for concept drift, and false negative refers to not alarming for concept drift. In this thesis, we introduce three algorithms, called as the Fast Hoeffding Drift Detection Method (FHDDM), the Stacking Fast Hoeffding Drift Detection Method (FHDDMS), and the McDiarmid Drift Detection Methods (MDDMs), for detecting drift points with the minimum delay, false positive, and false negative rates. FHDDM is a sliding window-based algorithm and applies Hoeffding's inequality (Hoeffding, 1963) to detect concept drift. FHDDM slides its window over the prediction results, which are either 1 (for a correct prediction) or 0 (for a wrong prediction). Meanwhile, it compares the mean of elements inside the window with the maximum mean observed so far; subsequently, a significant difference between the two means, upper-bounded by the Hoeffding inequality, indicates the occurrence of concept drift. The FHDDMS extends the FHDDM algorithm by sliding multiple windows over its entries for a better drift detection regarding the detection delay and false negative rate. In contrast to FHDDM/S, the MDDM variants assign weights to their entries, i.e., higher weights are associated with the most recent entries in the sliding window, for faster detection of concept drift. The rationale is that recent examples reflect the ongoing situation adequately. Then, by putting higher weights on the latest entries, we may detect concept drift quickly. An MDDM algorithm bounds the difference between the weighted mean of elements in the sliding window and the maximum weighted mean seen so far, using McDiarmid's inequality (McDiarmid, 1989). Eventually, it alarms for concept drift once a significant difference is experienced. We experimentally show that FHDDM/S and MDDMs outperform the state-of-the-art by representing promising results in terms of the adaptation and classification measures. Due to the evolving nature of data streams, the performance of an adaptive learner, which is defined by the classification, adaptation, and resource consumption measures, may fluctuate over time. In fact, a learning algorithm, in the form of a (classifier, detector) pair, may present a significant performance before a concept drift point, but not after. We define this problem by the question 'how can we ensure that an efficient classifier-detector pair is present at any time in an evolving environment?' To answer this, we have developed the Tornado framework which runs various kinds of learning algorithms simultaneously against evolving data streams. Each algorithm incrementally and independently trains a predictive model and updates the statistics of its drift detector. Meanwhile, our framework monitors the (classifier, detector) pairs, and recommends the efficient one, concerning the classification, adaptation, and resource consumption performance, to the user. We further define the holistic CAR measure that integrates the classification, adaptation, and resource consumption measures for evaluating the performance of adaptive learning algorithms. Our experiments confirm that the most efficient algorithm may differ over time because of the developing and evolving nature of data streams.