Ad Hoc wireless networks have been gaining importance in the communication world for the past decade. Wireless network extends the access to the network by removing the restriction of physical wires. Ad hoc network further improves the network coverage and availability to places without infrastructure support. Clock synchronization and dominating set are two of the fundamental issues in the wireless ad hoc networks. They are important for the correctness and/or performance of many protocols and applications. We focus on IEEE 802.11 wireless ad hoc networks in this dissertation due to the wide deployments of 802.11 networks. The theories and practices are definitely extensible to other types of ad hoc networks. IEEE 802.11 wireless network depends heavily on the distribution of timing information to all the stations in the network. Clock synchronization is important for frequency hopping, power saving and wireless medium reservation. We review the Timing Synchronization Function (TSF) of Ad Hoc mode defined in the 802.11 standard. It is well-known that the 802.11 TSF is not scalable. We carefully analyze the root causes of the scalability problem and design new schemes to overcome the problem. Our new schemes show great improvement over the 802.11 TSF and other solutions in the fields. Our solutions have nice characteristics: scalable, accurate, bounded and adaptive to station mobility. We are able to control the maximum clock differences under 25 micro seconds and 50 micro seconds in single hop and multihop networks respectively. The performance improvement is at least 200% or more compared with the current solutions. Dominating set has been widely used in multihop ad hoc networks (MANET) by numerous routing, broadcast and collision avoidance protocols. The problem to construct a minimum sized dominating set is known to be NP-hard. We propose a protocol that is simple, distributed, inexpensive, and adaptive to station mobility. We show that our protocol can construct dominating set using 35% to 60% less nodes than other distributed dominating set protocols. We study and address two of the fundamental and difficult problems in ad hoc wireless networks. Our solutions show significant improvements over the current solutions. Our work provides solid foundations to other important problems: routing, power saving, frequency hopping, media access scheduling, and broadcast storm mitigation.