We review recent results on the nonlinear development of thermal instability (TI) in the context of the turbulent atomic interstellar medium (ISM), in which correlated density and velocity fluctuations are present, as well as forces other than the thermal pressure gradient. First, we present a brief summary of the linear theory, remarking that, in the atomic ISM, the condensation mode is unstable but the wave mode is stable at small scales. Next, we revisit the growth of isolated entropy perturbations in initially unstable gas, as a function of the ratio of the cooling to the dynamical crossing times eta. The time for the dynamical transient state to subside ranges from 4 to 30 Myr for initial density perturbations of 20% and sizes 3 to 75 pc. When eta ≪ 1, the condensation produces locally supersonic motions and a shock propagates off the c ondensation, bringing the surrounding medium out of thermal equilibrium. Third, we consider the evolution of velocity perturbations, maintained by a random forcing, representing turbulent energy injection to the ISM from stellar sources. These perturbations correspond to the wave mode, and are stable at moderate amplitudes and small scales, as confirmed numerically. We then consider the behavior of magnetic pressure in turbulent regimes. Various observational and numerical results suggest that the magnetic pressure does not correlate well with density at low and intermediate densities. We propose that this is a consequence of the slow and fast modes of nonlinear MHD waves being characterized by different scalings of the magnetic field strength versus density. This lack of correlation suggests that, in fully turbulent regimes, the magnetic field may not be a very efficient source of pressure, and that polytropic descriptions of magnetic pressure are probably not adequate. Finally, we discuss simulations of the ISM (and resolution issues) tailored to investigate the possible existence of significant amounts of gas in the "lukewarm" temperature range between the warm and cold stable phases. The mass fraction in this range increases, and the phase segregation decreases, as smaller scales are considered. We attribute this to two facts: the enhanced stability of moderate, adiabatic-like velocity fluctuations with eta ≫ 1 and the recycling of gas from the dense to the diffuse phase by stellar energy injection. Moreover, the magnetic field is not strongly turbulent there, possibly providing additional stability. We conclude by suggesting that the gas with unstable temperatures can be observationally distinguished through simultaneous determination of two of its thermodynamic variables.