The continuous growth of global data transmission demands significantly higher channel capacity. According to Shannon’s theorem, an upper bound exists for the capacity of additive white Gaussian noise (AWGN) channels. This limit can be closely approached by optimizing conventional modulation schemes. Probabilistic shaping (PS) represents a critical technique to achieve this goal. By employing PS, the signal-to-noise ratio (SNR) gap between practical modulation formats and the Shannon limit can be reduced by up to 1.53dB. PS methods are generally categorized into direct and indirect schemes. Direct PS features low hardware complexity and high processing speed, making it suitable for long-blocklength and linear systems. In contrast, indirect PS can approach the Shannon limit more closely and is better adapted to medium-to-short blocklength and nonlinear scenarios. Nevertheless, it suffers from high hardware complexity and low computational efficiency. Given that direct PS has been well developed and widely deployed, while indirect PS still exhibits considerable room for improvement, future research will concentrate on the enhancement and optimization of indirect PS for nonlinear channel environments.