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We discuss intrinsic mechanisms of nonequilibrium excess noise in superconducting devices and transition edge sensors. In particular, we present an overview of fluctuation-driven contributions to the current noise in the vicinity of the superconducting transition. We argue that sufficiently close to the critical temperature fluctuations of conductivity may become correlated provided that the rate of quasiparticle relaxation is slow as compared to dynamics of superconducting fluctuations. In this regime, fluctuations of conductivity adiabatically follow the fluctuations of the electron distribution. This leads to a substantial enhancement of current noise. The corresponding spectral power density of noise has a Lorentzian shape in the frequency domain while its magnitude scales proportionally to the inelastic relaxation time. It also sensitively depends on the dephasing and Ginzburg-Landau timescales. Further estimates suggest that this mechanism dominates over the conventional temperature fluctuations in the same range of parameters. To describe these effects microscopically, we use the nonequilibrium Keldysh technique in the semiclassical approximation of superconductivity with Boltzmann-Langevin random forces to account for correlations of fluctuations.