After robust connectivity, precise positioning is evolving into an innovative component of 5G service offerings for industrial use-cases and verticals with challenging indoor radio environments. In this direction, the 3GPP Rel-16 standard has been a tipping point in specifying critical innovations, followed by enhancements in Rel-17 and Rel-18. In this article, we elaborate on the 5G positioning framework, measurements, and procedures before shifting the focus mainly to recently identified carrier-phase (CP) measurements in Rel-18 as a complementary measure for time- and angular-based positioning methods. We discuss the associated challenges and potential solutions for exploiting CP, including integer ambiguity, multipath sensitivity, and signaling aspects. Furthermore, we study how phase-continuous reference signaling can counter noisy phase measurements using realistic simulations to achieve centimeter-level accuracy in indoor factory (InF) scenarios.