Highly excited P and D states in 87Rb were examined using a two-step excitation procedure. A conventional rf lamp and a CW dye laser were used for the first and second step, respectively. The following results for the magnetic dipole interaction constant a, the electric quadrupole interaction constant b, the Landé gJ factor, and the tensor polarizability α2 were obtained in level-crossing and optical-double-resonance experiments:9 2P3/2: a = 4.05(3) MHz, b=0.55(3) MHz, gJ = 1.3335(15)10 2P3/2: a = 2.60(8) MHz, gJ = 1.3332(20)8 2D3/2: a = 2.840(15) MHz, b = 0.17(2) MHz8 2D5/2: a = -1.20(15) MHz, gJ = 1.1998(15)9 2D3/2: a = 1.900(10) MHz, b = 0.11(3) MHz9 2D5/2: a = (-)0.80(15) MHz, gJ = 1.1995(15), α2 = 180.3(9.0) MHz/(kV/cm)2Many-body calculations of the hyperfine structure of Rb have been performed. The polarization effect is included to all orders, whereas the correlation effect is omitted. The negative a factors for the 2D5/2 states, indicating large perturbations, are explained by the polarization contribution. A review of experimental hyperfine interaction constants, Landé gJ factors and tensor polarizabilities for rubidium is given together with theoretical values of the a factors. The quadrupole moment for 87Rb is obtained from the b factors for the 2P3/2 and 2D3/2 states, using quadrupole parameters from the many-body calculations. The correlation effect is included in a semi-empirical way.