We report on the two families of carbon materials (graphites and hard carbons) known to be the most attractive host structures in Li-ion batteries. Both present drawbacks related to the irreversible capacity. For graphites, it is due to exfoliation, which can be suppressed by the presence of the rhombohedral form. In fact, we show that some structure defects are responsible for this effect. For hard carbons, a clear correlation has been found between the irreversible capacity and the closed pore volume determined from helium pycnometry measurements.