Results are presented from analytical study and particle-in-cell simulations of the interaction of ultrashort petawatt laser pulses with underdense plasmas. It is shown that this interaction exhibits effects typical of the interaction of moderate-power pulses with overdense plasmas. The results obtained demonstrate relativistic self-focusing, the formation of a vacuum channel in a plasma, excitation of a superstrong longitudinal electric field, acceleration of ions and electrons up to ultrarelativistic energies, and generation of a quasistatic magnetic field. The generation of relativistic electromagnetic solitons is demonstrated. It is shown that a significant part of the laser-pulse energy is transformed into the energy of these solitons. The space and time dependences of the fields inside the solitons are found to agree with our analytical description.