This paper investigates the secondary multiuser diversity in spectrum sharing networks. We show that by exploiting the fading nature of interference links, the secondary system to efficiently utilize the spectrum while complying with constraints imposed by the primary system. More precisely, as the number of secondary users increases, the throughput grows logarithmically in a secondary multiple-access channel (MAC) and double-logarithmically in a secondary broadcast channel (BC). The multiuser diversity may also reduce the interference on the primary asymptotically to zero; the tradeoff between throughput enhancement and interference reduction is characterized. Finally, we results show that for the secondary MAC the growth rate of throughput decreases linearly with the number of primary users (constraints), while for the secondary BC the growth rate is unaffected by the number of primary constraints.