Mobile computing enables data transmission between devices without physical links, categorized into four types: fixed/wired, fixed/wireless, mobile/wired, and mobile/wireless. Key elements include mobile communication, hardware, and software, with challenges such as battery life, processing power, and security concerns. Wireless telephony, utilizing cellular networks, features handoff processes, location management, and communication standards like GSM, with advantages and disadvantages related to capacity, interference, and infrastructure needs.