The discovery of ultrafast demagnetization by Bigot and Beaurepaire in 1996 launched the field of ultrafast magnetism – the study of sub-picosecond magnetization dynamics in response to femtosecond laser excitations. In the same year, the discovery of spin-transfer torque switching of magnetic nanostructures [2,3] launched the field of spintronics – the control of magnetic order with electrical currents and voltage, germane to integrated electronic systems. Ultrafast magnetism may be particularly useful to future spintronic memory and logic devices by enabling magnetization switching at much faster time scales than in any existing spintronic technology. However, a number of obstacles stand in the way of integrating ultrafast magnetic phenomena into spintronic devices. To be useful for devices, ultrafast magnetization dynamics must be driven by electrical currents, not femtosecond lasers. The electrical currents need to be sourced by semiconductor transistors, which currently have a minimum gate delay on the order of picoseconds. Readout of the magnetic state must also be electrical, which will likely require a large magnetoresistance from a ferromagnetic tunnel junction. Finally, the switching energy must be minimized, which requires nanoscale device dimensions. This review discusses our most recent advances in addressing these challenges and bridging together the two fields of spintronics and ultrafast magnetism to enable the integration of ultrafast spintronic devices. Our research shows that, not only sub-picosecond optical pulses, but also picosecond excitations in the form of optical and electrical (heat current) pulses can result in the switching of the magnetization direction between two opposite states in ferrimagnetic GdFeCo. We also demonstrate ultrafast single shot switching of ferromagnetic Co/Pt exchange coupled to a GdFeCo layer. Furthermore, we observe ultrafast switching in nanoscale patterned GdCo dots. These achievements pave the way towards the construction of nanoscale ferromagnetic tunnel junctions capable of picosecond magnetization write times and electrical readout.