In this chapter deals with the identification of the temperature field, heat flux and heat transfer coefficient (HTC) based on the temperature measurement inside a body. The following methods of solving inverse heat conduction problems (IHCPs) are the subject of this chapter: exact solutions of inverse heat conduction problems, including the Burggraf method and the power series method. Methods for solving steady-state and transient IHCPs, both one-dimensional and multidimensional, are discussed extensively. Methods for solving linear and nonlinear IHCPs are described, and considerable attention is given to space-marching methods, which are simple and effective in solving linear and nonlinear steady-state and transient problems. The formulation and use of numerical-analytical methods of solving IHCPs and space marching methods are also presented in this chapter. Steady-state nonlinear inverse problems with the number of unknown parameters equal to the number of temperature measuring points and overdetermined problems were extensively illustrated using two-dimensional nonlinear IHCPs in cylindrical coordinates. Transient nonlinear overdetermined IHCPs were solved by the golden chapter search method in conjunction with future time interval. This approach to solving IHCPs is illustrated by the example of determining the transient temperature distribution in the wall of a pressurised water reactor vessel based on vessel wall temperatures measured at three different points along the wall thickness. The regularisation of the IHCPs to reduce the oscillation of the inverse solution over time is discussed at the end of the third chapter.