This article describes a polar phase-tracking receiver (PT-RX) architecture that can work with various modulations including differential phase shift keying (DPSK), amplitude phase shift keying (APSK), and quadrature amplitude modulation (QAM). By employing a two-point injection method in a wideband digital phase-locked loop (DPLL), the proposed polar PT-RX performs various demodulations without requiring quadrature signal generation or a multi-bit analog-to-digital converter (ADC). Compared with existing PT-RXs, the proposed architecture not only overcomes the trade-off between frequency pulling and image rejection but also provides the equivalent constant gain of a digitally controlled oscillator (DCO) for robust demodulation. A prototype 5.8-mW 2.4-GHz polar PT-RX is implemented in 65-nm CMOS and performs demodulations of 8-DPSK at 1.5 Mb/s, 16-QAM at 2 Mb/s and 32-APSK at 2.5 Mb/s, achieving a sensitivity of ?81, - 68, and ?64 dBm, respectively.