Fiber lasers mode locked with large normal group-velocity dispersion have recently achieved femtosecond pulse durations with energies and peak powers at least an order of magnitude greater than those of prior approaches. Several new mode-locking regimes have been demonstrated, including self-similar pulse propagation in passive and active fibers, dissipative solitons, and a pulse evolution that avoids wave breaking at high peak power but has not been reproduced by theoretical treatment. Here, we illustrate the main features of these new pulse-shaping mechanisms through the results of numerical simulations that agree with experimental results. We describe the features that distinguish each new mode-locking state and explain how the interplay of basic processes in the fiber produces the balance of amplitude and phase evolutions needed for stable high-energy pulses. Dissipative processes such as spectral filtering play a major role in normal-dispersion mode locking. Understanding the different mechanisms allows us to compare and contrast them, as well as to categorize them to some extent.