High entropy alloys (HEAs) with a face-centered cubic (fcc) structure have received an increasing attention in recent years due to their exceptional ductility and fracture toughness. On the other hand, they generally show lower strengths at ambient and elevated temperatures. In this review, we attempt to highlight recent advances in the design of computation-aided HEAs being alloyed with Al, Al/Ti, Nb and Mo additions on the precipitation hardening behavior of this fcc-type CoCrFeNi alloy, and to summarize the corresponding mechanical properties of the newly developed precipitation-strengthened HEAs under different thermomechanical processing. In particular, our emphasis is played on elucidating the correlation between precipitation behaviors and mechanical properties, which may serve as a demonstrative summary for the current progress in the scientific research of precipitation-strengthened HEAs. Finally, future research areas for these precipitation-strengthened HEAs are critically assessed.