Controlling quantum systems with high fidelity is an essential prerequisite in various fields, such as coherent control of atomic and molecular systems and quantum information processing. Between the strategies developed for these purposes, for a Hamiltonian whose temporal change is slow, the adiabatic theorem guarantees that if the system starts in one of the instantaneous eigenstates, then it will follow this state closely. Within the last few years a large theoretical effort developed specific time-dependent Hamiltonian transformations, named transitionless- superadiabatic-transitionless protocols or shortcuts to adiabaticity, aimed to improve the fidelity of the adiabatic quantum transfer and its speed(1-3). Experimental investigations have implemented those protocols. Using a two-level quantum system based on Bose–Einstein condensates in a 1D optical lattice, we have implemented transitionless-superadiabatic protocols in which the system follows the instantaneous adiabatic ground state nearly perfectly(4). We have tested a superadiabatic protocol reaching the maximum quantum-transformation speed compatible with the Heisenberg uncertainty principle and extremely robust against control parameter variations. Experimental realizations by other research groups will be also briefly discussed. The superadiabatic transformations make it possible to readily implement protocols ensuring near-perfect adiabatic following in a variety of existing applications. (1) R. Lim and M.V. Berry, J. Phys. A 24, 3255 (1991); M.V. Berry, J.Phys. A 42, 365303 (2009).(2) M. Demirplak, and S.A. Rice, J. Phys. Chem. A 107, 9937 (2003), and J. Chem. Phys. 129, 154111 (2008).(3) J. G Muga, et al., J. Phys. B: At. Mol. Opt. Phys. 43 085509 (2010).(4) M.G. Bason, et al, Nature Physics 8, 147 (2012).