Amplitudes and Cross Sections at the LHC

We describe the elements of the GLM model that successfully describes soft hadronic interactions at energies from ISR to LHC. This model is based on a single Pomeron with a large intercept $\Delta_{\pom}$ = 0.23 and slope $\alpha_{\pom}'$ = 0, and so provides a natural matching with perturbative QCD. We analyze the elastic, single diffractive and double diffractive amplitudes, and compare the behaviour of the GLM amplitudes to those of other parameterizations. We summarize the main features and results of competing models for soft interactions at LHC energies.