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The field of quantum information has inspired new methods for cooling physical systems at the quantum scale, such as heat-bath algorithmic cooling. These methods not only provide fundamental insight into quantum thermodynamics, they are a practical method to improve the purity of initial states required in implementing quantum algorithms, as well as to provide a reliable low-noise supply of ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction. In this talk, I will first review the basic ideas of algorithmic cooling and give analytical results for the achievable cooling limits for the conventional heat-bath version. Then, I will show how the limits can be circumvented by using correlations. In one algorithm I take advantage of correlations that can be created during the rethermalization step with the heat-bath and in another I use correlations present in the initial state induced by the internal interactions of the system. These two algorithms show how correlations can be used to improve cooling.