We study experimentally the electron transport properties of gated quantum dots formed in InGaAs/InP and InAsP/InP quantum well structures grown by chemical-beam epitaxy. For the case of the InGaAs quantum well, quantum dots form directly underneath narrow gate electrodes due to potential fluctuations. We measure the Coulomb-blockade diamonds in the few-electron regime of a single quantum dot and observe photon-assisted tunneling peaks under microwave irradiation. A singlet-triplet transition at high magnetic field and Coulomb-blockade effects in the quantum Hall regime are also observed. For the InAsP quantum well, an incidental triple quantum dot forms also due to potential fluctuations within a single dot layout. Tunable quadruple points are observed via transport measurements.