The standard model has been highly successful at describing current experimental data. However, extensions of the standard model predict particles that have masses at energy scales that are above the electroweak scale. The flavor-changing neutral current processes of the B meson are sensitive to the influences of these new physics contributions. These processes proceed through loop diagrams, thus allowing new physics to enter at the same order as the standard model. New physics may contribute to the enhancement or suppression of rate asymmetries or the decay rates of these processes. The transition B {yields} V{gamma} (V = K*(892), {rho}(770), {omega}(782), {phi}(1020)) represents radiative decays of the B meson that proceed through penguin processes. Hadronic uncertainties limit the theoretical accuracy of the prediction of the branching fractions. However, uncertainties, both theoretical and experimental, are much reduced when considering quantities involving ratios of branching fractions, such as CP or isospin asymmetries. The most dominant exclusive radiative b {yields} s transition is B {yields} K*{gamma}. We present the best measurements of the branching fractions, direct CP, and isospin asymmetries of B {yields} K*{gamma}. The analogous b {yields} d transitions are B {yields} {rho}{gamma} and B {yields} {omega}{gamma}, which are suppressed by a factor of |V{sub td}/V{sub ts}|{sup 2} {approx} 0.04 relative to B {yields} K*{gamma}. A measurement of the branching fractions and isospin asymmetry of B{sup +} {yields} {rho}{sup +}{gamma} and B{sup 0} {yields} {rho}{sup 0}{gamma}, as well as a search for B {yields} {omega}{gamma}, are also given. These measurements are combined to calculate the ratio of CKM matrix elements |V{sub td}/V{sub ts}|, which corresponds to the length of one side of the unitary triangle. Finally, we present a search for the penguin annihilation process B {yields}{phi}{gamma}. We use a sample of 383 million B{bar B} events collected with the BABAR detector at the PEP-II asymmetric-energy B factory for the analysis of B {yields} K*{gamma}. We measure the branching fractions {Beta}(B{sup 0} {yields} K*{sup 0}{gamma}) = (4.47 {+-} 0.10 {+-} 0.16) x 10{sup -5} and {Beta}(B{sup +} {yields} K*{sup +}{gamma}) = (4.22 {+-} 0.14 {+-} 0.16) x 10{sup -5}. We measure the direct CP asymmetry to be -0.033 < {Alpha}{sub CP} (B {yields} K*{gamma}) < 0.028 and the isospin asymmetry to be 0.017 < {Delta}{sub 0-} < 0.116, where the limits are determined at the 90% C.L. and include both the statistical and systematic uncertainties. Using a sample of 347 million B{bar B} events, we measure the branching fractions {Beta}(B{sup +} {yields} {rho}{sup +}{gamma}) = (1.10{sub -0.33}{sup +0.37} {+-} 0.09) x 10{sup -6} and {Beta}(B{sup 0} {yields} {rho}{sup 0}{gamma}) = (0.79{sub -0.20}{sup +0.22} {+-} 0.06) x 10{sup -6}, the isospin asymmetry {Delta} = -0.35 {+-} 0.27, and set a 90% C.L. upper limit {Beta}(B {yields} {omega}{gamma}) < 0.78 x 10{sup -6}. We also measure the isospin-averaged branching fraction {Beta}(B {yields} ({rho}/{omega}){gamma}) = (1.25{sub -0.24}{sup +0.25} {+-} 0.09) x 10{sup -6}, from which we determine |V{sub td}/V{sub ts}|= 0.200{sub -0.020}{sup +0.021} {+-} 0.015, where the first uncertainty is experimental and the second theoretical. Finally, a sample of 124 million B{bar B} events is used to set an upper limit of {Beta}(B {yields} {phi}{gamma}) < 8.5 x 10{sup -7} at the 90% C.L.