Summary: This paper presents an adaptive scheme for localization of a target from distance measurements and motion control of a mobile agent to pursue this target. The localization and motion control task of interest is approached within a parameter-identifier-based adaptive control framework, where the localization is formulated as a parameter identification problem and the motion control is achieved using an adaptive controller based on the produced location estimates of the target. First, a robust adaptive law is designed to generate location estimate of the target using distance measurements. Then, following the standard certainty equivalence approach, a motion control law is developed considering substitution of the estimate generated by the localization algorithm for the unknown location of the target. Noting that there is some incompatibility between the persistence of excitation requirements of the localization algorithm and the target pursuit goal of the motion control law, the base motion control law is (re)designed to eliminate the effects of this incompatibility. The novelty of this paper is in this motion control design eliminating the persistence of excitation incompatibility. Stability and convergence analysis for the overall adaptive control scheme is presented. The results are valid in both two and three dimensions of motion space. The applications of the adaptive scheme include rescue localization, surveillance of signal sources, and formation acquisition of autonomous multi-robot/vehicle systems.