In this talk I am going to discuss various aspects of low dimensional quantum magnets with random interactions including Heisenberg model on spin chains and square lattices, as well as impurity doped spin-Peierls systems which, at low doping and low temperature, can be described as random antiferromagnets. Most of the results that I will present have been obtained with the help of very large scale numerical simulations (i.e. quantum Monte Carlo simulations, Exact Diagonalizations, Numerical Real Space RG).

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