Demand for increasing performance is far outpacing the capability of traditional methods for performance scaling. Disruptive solutions are needed to advance beyond incremental improvements. Traditionally, processors reside inside packages to enable PCB-based integration. We argue that packages reduce the potential memory bandwidth of a processor by at least one order of magnitude, allowable thermal design power (TDP) by up to 70%, and area efficiency by a factor of 5 to 18. Further, silicon chips have scaled well while packages have not. We propose packageless processors - processors where packages have been removed and dies directly mounted on a silicon board using a novel integration technology, Silicon Interconnection Fabric (Si-IF). We show that Si-IF-based packageless processors outperform their packaged counterparts by up to 58% (16% average), 136%(103% average), and 295% (80% average) due to increased memory bandwidth, increased allowable TDP, and reduced area respectively. We also extend the concept of packageless processing to the entire processor and memory system, where the area footprint reduction was up to 76%.