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Transient surveys across the electromagnetic spectrum have revolutionized our understanding of explosive astrophysical phenomena. While typical core-collapse supernovae are thought to be powered by neutrino emission from a proto-neutron star (the neutrino-driven explosion scenario), several classes of exceptionally bright and/or energetic supernovae challenge this standard model. Notable examples include broad-lined Type Ic supernovae associated with gamma-ray bursts and superluminous supernovae. These events are believed to be powered by more exotic central engines, such as fast-spinning magnetars or black hole accretion disks. Electromagnetic observations of this extreme supernova population offer a unique opportunity to probe their underlying physics and possibly identify their true power sources. In this talk, I will introduce these bright supernovae and present numerical studies I have conducted to investigate their origins and mechanisms.