Abstract: For the last half-century, relativistic outflows accompanying the final collapse of massive stars have predominantly been detected via high-energy emission, as long-duration gamma-ray bursts (GRBs). From wide-field optical and radio time-domain surveys, there have been hints of related phenomena at lower energies, such as X-ray flashes. With the Zwicky Transient Facility (ZTF) we are conducting a systematic exploration of the broader landscape of engine-driven explosions, of which traditional GRBs are just one manifestation. The emerging zoo includes afterglows at cosmological distances with no detected GRB, broad-lined Ic (Ic-BL) supernovae with luminous X-ray and radio emission, and fast-luminous transients powered by circumstellar interaction such as AT2018cow. Understanding the origin of these events and their relation to GRBs will require coordinated observations between high-cadence optical surveys, wide-field gamma-ray monitors, and millimeter and radio observatories. This will be possible in the next few years with the launch of the Space-based multi-band astronomical Variable Objects Monitor (SVOM), the enhanced cadence of ZTF Phase II, and sensitive millimeter-band facilities like the Atacama Large Millimeter Array (ALMA).