In this presentation, we will investigate the support properties of solutions to nonlinear stochastic heat equations with random noise. The noise may be either space-time white noise or spatially homogeneous colored noise satisfying the reinforced Dalang’s condition. We will introduce conditions on the diffusion coefficient that guarantee the compact support property and strictly positive of solutions. Moreover, we will propose potential extensions of these conditions. This work is a collaboration with Kunwoo Kim and Jaeyun Yi.