For gradual SEP events, the self-generated turbulence around CME-driven shocks may be important. Theoretical modeling has pointed out a few possible mechanisms: the particles escape before large wave growth occurs, adiabatic focusing in the diverging magnetic field, and/or the shock arriving at a region less favorable to wave growth. On the other hand, if strong turbulence exists in the corona (i.e., not self-generated), particle acceleration and escape are likely to be consecutive processes. For impulsive SEP events, self-generated turbulence is likely to be weak, and escape will depend on the SEPs reaching magnetic field lines connected to the heliosphere. Timing, compositional, spectral and anisotropy observations for SEPs, together with in situ wave and magnetic field measurements close to the Sun and field line tracking are key to discriminating between escape mechanisms.