Permutationally Invariant Quantum Tomography is a procedure that has been developed mostly for states that are close to being permutationally symmetric, which is typical in nowadays experiments. For two-state particles, the number of measurements needed scales only quadratically with the number of particles. Besides the modest measurement effort, the processing of the measured data can also be done efficiently: It is possible to carry out the fitting of a physical density matrix on the measured data even for large systems. Permutationally Invariant Quantum Tomography has been combined with compressed sensing in a six-qubit photonic experiment.