Carrier phase recovery (CPR) is a key digital signal processing (DSP) subsystem in optical fiber communications. In this paper, we review recent advances in CPR algorithms and analyze their performance under the impact of different system impairments in a long-haul 256 GBaud setting. We study both single- and dual-stage CPR configurations, in the linear and nonlinear regimes, and at different system baud rates. By exploiting CPR algorithms tailored for digital subcarrier multiplexing (DSCM) systems, we are able to reap the benefits of their intrinsic resilience to the two main performance-limiting effects of optical fiber systems: equalization enhanced phase noise (EEPN) and nonlinear interference (NLI). Overall, the paper sheds light on the potential benefits of DSCM and highlights the need for further research into CPR algorithms that specifically target the effect of nonlinear phase noise (NLPN).