High-throughput and low-latency sorting is a key requirement in many applications that deal with large amounts of data. This paper presents efficient techniques for designing high-throughput, low-latency sorting units. Our sorting architectures utilize modular design techniques that hierarchically construct large sorting units from smaller building blocks. The sorting units are optimized for situations in which only the M largest numbers from N inputs are needed, because this situation commonly occurs in many applications for scientific computing, data mining, network processing, digital signal processing, and high-energy physics. We utilize our proposed techniques to design parameterized, pipelined, and modular sorting units. A detailed analysis of these sorting units indicates that as the number of inputs increases their resource requirements scale linearly, their latencies scale logarithmically, and their frequencies remain almost constant. When synthesized to a 65-nm TSMC technology, a pipelined 256-to-4 sorting unit with 19 stages can perform more than 2.7 billion sorts per second with a latency of about 7 ns per sort. We also propose iterative sorting techniques, in which a small sorting unit is used several times to find the largest values.