Deep learning models trained in a supervised setting have revolutionized audio and speech processing. However, their performance inherently depends on the quantity of human-annotated data, making them costly to scale and prone to poor generalization under unseen conditions. To address these challenges, Self-Supervised Learning (SSL) has emerged as a promising paradigm, leveraging vast amounts of unlabeled data to learn relevant representations. The application of SSL for Automatic Speech Recognition (ASR) has been extensively studied, but research on other downstream tasks, notably Speaker Recognition (SR), remains in its early stages. This work describes major SSL instance-invariance frameworks (e.g., SimCLR, MoCo, and DINO), initially developed for computer vision, along with their adaptation to SR. Various SSL methods for SR, proposed in the literature and built upon these frameworks, are also presented. An extensive review of these approaches is then conducted: (1) the effect of the main hyperparameters of SSL frameworks is investigated; (2) the role of SSL components is studied (e.g., data-augmentation, projector, positive sampling); and (3) SSL frameworks are evaluated on SR with in-domain and out-of-domain data, using a consistent experimental setup, and a comprehensive comparison of SSL methods from the literature is provided. Specifically, DINO achieves the best downstream performance and effectively models intra-speaker variability, although it is highly sensitive to hyperparameters and training conditions, while SimCLR and MoCo provide robust alternatives that effectively capture inter-speaker variability and are less prone to collapse. This work aims to highlight recent trends and advancements, identifying current challenges in the field.