It is believed that quantum computing can provide advantage over classical computing by exploiting superposition and entanglement. However, presence of noise in the near-term devices poses obstacles to efficiently utilizing quantum computing. Scientists have been working on various techniques to characterize and mitigate the noise in quantum devices. In this talk I will start with an overview of quantum computing and then mention our work in collaboration with researchers at BNL, in which we characterize the readout process of IBM quantum computers, and how the results can be used to mitigate readout errors. In addition to the readout errors, there are other errors associated with state preparation and quantum gates, potentially with spatial and/or temporal crosstalk. Consequently, characterization becomes challenging as the circuit becomes large. To address the overall noise present in quantum circuits, we introduce a method to characterize circuit performance, which remains efficient even for large circuits. In the end I will outline a few challenges ahead, such as scalability in the error characterization/mitigation and the impact of noise on some near-term applications of quantum computing.