Internal transport barriers (ITBs), marked by a steep density profile, even stronger peaking in the pressure profile and reduction of core transport are obtained in Alcator C-Mod. They are induced by the use of off-axis D(H) ICRF (ion cyclotron range of frequencies) power deposition. They also arise spontaneously in Ohmic H-mode plasmas once the H-mode lasts for several energy confinement times. Recent studies have explored the limits for forming, maintaining and controlling these plasmas. The C-Mod provides a unique platform for studying such discharges: the high density (up to 8 × 1020 m−3) causes the ions and electrons to be tightly coupled by collisions with Ti/Te = 1, and the plasma has no internal particle or momentum sources. The ITBs formed in both Ohmic and ICRF heated plasmas are quite similar regardless of the trigger method. Control of impurity influx and heating of the core plasma in the presence of the ITB have been achieved with the addition of central ICRF power, in both Ohmic H-mode and ICRF induced ITBs. Control of the radial location of the transport barrier is achieved through manipulation of the toroidal magnetic field and plasma current. A narrow region of decreased electron thermal transport, as determined by sawtooth heat pulse analysis, is found in these plasmas as well. Transport analysis indicates that reduction of the particle diffusivity in the barrier region allows the neoclassical pinch to drive the density and impurity accumulation in the plasma centre. Examination of the gyro-kinetic stability indicates that the density and temperature profiles of the plasma core are inherently stable to long-wavelength drift mode driven turbulence at the onset time of the ITB, but that the increasing density gradients cause the trapped electron mode to play a role in providing a control mechanism to ultimately limit the density and impurity rise in the plasma centre.