The new insights into a) the rapidly varying structures of neutron-rich nuclei up to spins as high as 20(+) and 19(-), b) the spontaneous fission process itself, and c) modes of cluster radioactivity that have come out of studies of spontaneous fission of Pu-242, Cm-248 and Cf-252 with large detector arrays are presented. The studies include gamma-gamma-gamma coincidences with the second generation (14-20 Compton-suppressed Ge arrays) and new, third generation (35-45 Compton-suppressed Ge arrays, Gammasphere and Eurogam) gamma-ray detector arrays. The neutron-rich nuclei observed span the full range from superdeformed (beta (2) greater than or equal to 0.4) double-magic ground states to spherical double-magic nuclei and competing shapes in between. New structure insights include the following: New regions of identical ground state bands to spins of 10(+) to 16(+) were discovered; one at the sudden onset of large deformation at N=60,62 in both even- and odd-A Sr-98-101, one at midshell N=64,66 in Ru-108,Ru-110, one for N=88-90 Ba-144,Ba-146, one for N=92-94 Nd-152,Nd-154, and at high spin in Nd-156 also in excited bands in these regions. New shape coexisting structures in both even- and odd-A for A=96-102 Sr and Zr nuclei are found. Evidence is found in both even-even and odd-A nuclei for a new region of octupole deformation around Z=56 and N=86-88. Rapid changes in moments of inertia are observed with changes in Z and N of two units with sudden changes in the moments of inertia associated with band crossings. The levels in many neutron-rich nuclei are observed for the first time. Earlier, plunger studies yielded lifetimes of low spin states and recently the Doppler Shift Line Shape Analysis yielded lifetimes of high spin states, For the first time, direct measurements of yields and neutron multiplicities have been made for five correlated pairs of fission fragments of Sr-Nd, Zr-Ce, Mo-Ba, Ru-Xe and Pd-Te nuclei. Neutron multiplicities from 0-10 v emission (10v for the first time) were observed in MoBa correlated pairs with the 0 and 7-10 neutron-emission yields enhanced compared to gross yields for all fragments. The Mo-Ba data provide evidence for two different fission modes. By unfolding the observed Mo-Ba yields, the masses and excitation energies and mass distributions at scission were extracted. These data revealed a new mode involving the high neutron multiplicities that occurs essentially through one pair, Mo-108-Ba-144, Mo-107-Ba-145, or Mo-106-Ba-146 or some combination where the Ba-144, Ba-145 and/or Ba-146 at scission are hyperdeformed with a long-to-short axis ratio of 3:1. The zero-neutron emission channels provide new examples of the cold rearrangements of nucleons in a new type of cluster radioactivity. The cluster radioactivity model predicted the observed enhancements of the zero-neutron channels for odd-A-odd-A nuclei as well as the observed fine structure, that is, the spin distributions of the two fragments. The measurements of intensities and gamma-gamma-gamma coincidences in SF with large detector arrays open a new era in the determination of previously inaccessible properties of neutron-rich nuclei and the fission process.