Cyclic redundancy check (CRC) aided polar codes are capable of achieving better performance than low-density parity-check (LDPC) codes under the successive cancelation list (SCL) decoding scheme. However, the SCL decoding scheme suffers from very high space and time complexities. Especially, the high space complexity is a major concern for adopting polar codes in modern mobile communication standards. In this paper, we propose a novel reduced-complexity successive cancelation list (R-SCL) decoding scheme which is effective to reduce the space complexity. Simulation results show that, with a (2048, 1024) CRC-aided polar code, the R-SCL decoders with 25% reduction of space complexity and 8% reduction of time complexity can still achieve almost the same performance levels as those decoded by SCL decoders. To further reduce the complexity, we propose a multi-CRC coding scheme for polar codes. Simulation results show that, with a (16384, 8192) multi-CRC-aided polar code, a R-SCL decoder with about 85% reduction of space complexity and 20% reduction of time complexity results in a worst performance loss of only 0.04dB.