Employing low-resolution analog-to-digital converters (ADCs) for millimeter-wave receivers with large antenna arrays provides an opportunity to efficiently reduce power consumption of the receiver. Reducing ADC resolution, however, results in performance degradation due to non-negligible quantization error. In addition, the large number of radio frequency chains is still not desirable. Accordingly, conventional low-resolution ADC systems require more efficient designs to minimize the cost and complexity while maximizing performance. In this article, we discuss advanced low-resolution ADC receiver architectures that further improve the spectral and energy efficiency trade-off. To reduce both the numbers of RF chains and ADC bits, hybrid analog and digital beamforming is jointly considered with low-resolution ADCs. We explore the challenges in designing such receivers and present key insights on how the advanced architectures overcome such challenges. As alternative low-resolution ADC receivers, we also introduce receivers with learning-based detection. The receiver does not require explicit channel estimation, and thus is suitable for one-bit ADC systems. Finally, future challenges and research issues are discussed.