It has been recently shown that a limited form of error correction for shallow quantum circuits can be achieved by combining outcomes of multiple noisy experiments in a way that negates the effect of noise. These methods, collectively known as Quantum Error Mitigation (QEM), are well suited for quantum devices available today because they introduce little or no overhead in the number of qubits. In this talk I will discuss recent progress on QEM with a focus on the quasi-probability methods. First, it is shown that QEM can be naturally integrated into the standard surface code architecture to implement logical T-gates. As a result, logical Clifford+T circuits with a number of T-gates inversely proportional to the physical noise rate can be implemented on small error-corrected devices without magic state distillation. Secondly, I will discuss how to mitigate readout errors introduced by imperfect qubit measurements. Such errors are often the dominant factor limiting scalability of near-term devices.