Employing low-resolution analog-to-digital converters (ADCs) for millimeter wave receivers with large antenna arrays provides 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 (RF) 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 tradeoff. 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 an alternative low-resolution ADC receiver, we also introduce receivers with learning-based detection. The receiver does not require explicit channel estimation, thereby is suitable for one-bit ADC systems. Finally, future challenges and research issues are discussed.