Most materials including concrete have pre-existing flaws or defects. The fracture energy of concrete is a basic material property needed to understand fracture initiation and propagation in concrete. Whether fracture energy is size dependent or not is being discussed world over. Strictly the fracture energy if taken as a material property should be constant, and should be independent of the method of measurement, test methods, specimen shapes and sizes. A computational study on simulation of fracture in concrete using two dimensional lattice models is presented. A comparison is made with acoustic emission (AE) events with the number of fractured elements. A three-point bend specimen (TPB) is modeled using regular triangular lattice network. It was observed that the number of fractured elements increases near the peak load and beyond the peak load. AE events also increase rapidly beyond the peak load. Singular Fractal Functions (S.F.F) has been employed to interpret the size effect of quasi-brittle materials like concrete. The usual size dependent fracture energy of High Strength Concrete (HSC) beam is reported. The results are presented which are obtained directly from the experiments related to size effect in concrete carried out in the Structural engineering laboratory, Department of Civil engineering, IISc. Various fracture parameters studied in this experimental program are (a) Nominal strength N (b) Fracture energy, Gf (c)Fracture toughness, KIc, (c) Crack mouth opening displacement, CMOD (d) Size effect on the strength of concrete. Three-point-bend (TPB) specimen was chosen for the experimental study. Six different concrete mixes viz. A-mix, B-Mix, C-mix, D-Mix, E-mix, F-Mix were used. Acoustic Emission (AE) experiments are conducted to relate acoustic emission energy to fracture energy. It is interesting to note that both acoustic emission energy and fracture energy have similar characteristics. The advantage of the above relationship is that now it is possible to evaluate fracture energy by non-destructive testing methods. The b-value analysis of AE was carried out to study the damage in concrete structures. The Guttengberg-Richter relation for frequency versus magnitude can be applied to the AE method to study the scaling of the amplitude distribution of the acoustic emission waves generated during the cracking process in the test specimen at laboratory or in engineering structures. In the next part of this chapter b-value at various stages of damage of a reinforced concrete beam are obtained experimentally under typical cyclic loadings. The b-values at different levels of damage are tabulated. As fracture is size dependent, it may not be very useful unless its size dependency is eliminated. An effort is made to obtain size independent fracture energy by a hybrid technique.