Recent advancements in additive manufacturing have rendered the creation of conformal cooling channels more accessible and cost-effective. In the injection molding process, conformal cooling channels offer enhanced cooling efficiency relative to traditional straight-drilled channels. The major reason is that conformal cooling channel can adhere to the contours of the molded geometry, but conventional machining methods cannot. Using conformal cooling channel can reduce thermal stresses and distortion, improve cycle time, and provide a more consistent temperature distribution. Conversely, traditional channels use a more complex design method than conformal cooling channel. Simulations of computer-aided engineering (CAE) are essential for developing an efficient and economical design. Design and/or topology optimization techniques can be used to reach optimal solutions. This paper reviews the fundamental methodologies for the design and topology optimization of Conformal Cooling Channels (CCCs) in injection molds. This article aims to present the most relevant optimization techniques that may be used for the optimization of conformal cooling channels in injection molds, to be used as a guide for engineers to be able to select the best optimization method according to the objectives of their project(s). The results highlight the significant advantages of CCC in injection molding, particularly in reducing cooling time, improving thermal uniformity, and enhancing part quality. The comparative analysis of optimization techniques presented provides valuable insights for selecting the most effective method based on project objectives, whether focusing on design complexity, computational efficiency, or real-world validation. Additionally, the integration of computational simulations, optimization algorithms, and experimental validation underscores the importance of a multi-faceted approach in achieving optimal conformal cooling channels' performance. These findings aim to be useful as a practical guide for engineers and researchers aiming to enhance injection molding efficiency through advanced cooling channel design.