In this chapter we study the backreaction problem in early universe cosmology, i.e., finding solutions to the semiclassical Einstein equation, which is at the heart of semiclassical gravity theory. Four groups of backreaction problems at the Planck and grand unified theory scales are presented. (1) Effects of the trace anomaly (a) in facilitating possible avoidance of singularity and (b) in engendering inflation, as in the so-called Starobinsky inflation. (2) Effects of particle creation on cosmological singularity and particle horizons, in affecting the equation of state of matter, and in the damping of anisotropy or inhomogeneity. (3) For inflationary cosmology, post-inflationary preheating by the dissipative effects of particle creation and interaction from the nonequilibrium inflaton dynamics, using an O(N) Phi-4 theory as an example. (4) We also mention backreaction problems in stochastic inflation, where the short wavelength modes acting as noise backreact on the long wavelength modes, thereby decohering the latter into classical background modes (5) In terms of quantum cosmology, we consider the validity of minisuperspace approximation by studying the effect of inhomogeneous modes on the homogeneous mode in a Phi-4 model.