Nuclear spins dynamics recently gained prominence for semiconductor quantum information technologies. At least two rami cations can be mentioned within this context: rst, as a decoherence channel for carrier spin qubit stored in a quantum dot, and second as a potential quantum memory with the proviso that the nuclear spin bath can be tamed. To shed light on either of these matters, this thesis presents numerical simulations of spin dynamics of quadrupolar nuclei which constitute a large fraction of group III-V semiconductors. Particular attention is devoted to the electric quadrupole interaction that prevail in these strained semiconductor structures. Within Lindblad master equation formalism, the saturation under an incoherent radio frequency pump, and subsequent relaxation of spin-3/2 nuclei are studied. The quadrupole interaction does not manifest itself via a conspicuous ngerprint in these processes other than causing faster relaxation. However, we identify that its prime role is in spin squeezing. The characteristics of all spins between 1/2 to 9/2 have been thoroughly investigated under one-axis, mixed-axis, and two-axis countertwisting conditions. Our main conclusion is that the presence of quadrupole interaction substantially degrades the average level of squeezing, which further complicates the quantum control of nuclear spin bath uctuations.