This paper presents mathematical modelling of telegraph equations and as an application of transmission lines in electrical signals and gives a survey of the results on the development of numerical methods for solving telegraph equations with both constant and variable coefficients. A tutorial work on which methods are more advantageous among the present numerical methods has not been studied in the literature except a few works discussing some specific methods. The purpose of this paper is to fill this gap by including the examination of some advantages and disadvantages of numerical methods for solving telegraph equations with time and/or space variable coefficients with their various aspects. A general modelling of power transmission lines is also presented in this paper. Moreover, various open problems are discussed for the future development of numerical methods for the analysis of telegraph equations.