Advanced theoretical methods and high-performance computers may finally unlock the secrets of nuclear fission, a fundamental nuclear decay that is of great relevance to society. In this work, we studied the phenomenon of spontaneous fission using the symmetry-unrestricted nuclear density functional theory (DFT). Our results show that many observed properties of fissioning nuclei can be explained in terms of pathways in multidimensional collective space corresponding to different geometries of fission products. From the calculated collective potential and collective mass, we estimated spontaneous fission half-lives, and good agreement with experimental data was found. We also predicted a new phenomenon of trimodal spontaneous fission for some transfermium isotopes. Our calculations demonstrate that fission barriers of excited superheavy nuclei vary rapidly with particle number, pointing to the importance of shell effects even at large excitation energies. The results are consistent with recent experiments where superheavy elements were created by bombarding an actinide target with 48-calcium; yet even at high excitation energies, sizable fission barriers remained. Not only does this reveal clues about the conditions for creating new elements, it also provides a wider context for understanding other types of fission. Understanding of the fission process is crucial for many areas of science and technology. Fission governs existence of many transuranium elements, including the predicted long-lived superheavy species. In nuclear astrophysics, fission influences the formation of heavy elements on the final stages of the r-process in a very high neutron density environment. Fission applications are numerous. Improved understanding of the fission process will enable scientists to enhance the safety and reliability of the nation's nuclear stockpile and nuclear reactors. The deployment of a fleet of safe and efficient advanced reactors, which will also minimize radiotoxic waste and be proliferation-resistant, is a goal for the advanced nuclear fuel cycles program. While in the past the design, construction, and operation of reactors were supported through empirical trials, this new phase in nuclear energy production is expected to heavily rely on advanced modeling and simulation capabilities.