Charged fluorescent bowl‐shaped colloids consisting of a polystyrene core surrounded by a poly(N‐isopropylmethacrylamide) shell are obtained by nanoengineering spherical composite microgels. The phase diagram of these soft bowl‐shaped colloids interacting through long‐range Yukawa‐type interactions is investigated using confocal laser scanning microscopy. The bowl‐shaped structure leads to marked differences in phase‐behavior compared to their spherical counterpart. With increasing number density, a transition from a fluid to a plastic crystal phase, with freely rotating particles, followed by a glass‐like state is observed. It is found that the anisotropic bowl shape frustrates crystallization and slows down crystallization kinetics and causes the glass‐like transition to shift to a significantly lower volume fraction than for the spheres. Quantitative analysis of the positional and orientational order demonstrates that the plastic crystal phase exhibits quasi‐long range translational order and orientational disorder, while in the disordered glass‐like phase the long‐range translational order vanishes and short‐range rotational order appears, dictated by the specific bowl shape. It is further shown that the different structural transitions are characterized by decoupling of the translational and orientational dynamics. The phase behavior of bowl‐shaped colloids interacting via a long‐range Yukawa potential is compared to their spherical counterpart. The formation of a plastic crystal and glass‐like phase is observed at low‐volume fractions. Using a novel tracking algorithm, the order and dynamics of these anisotropic colloids in the phases is investigated in detail.