<p>This study proposes an extensive review of photonics crystal-based logic devices, essential for all-optical Arithmetic and Logic Units. This review takes into account the literature that has been published in the past couple of decades. Depending on how they function in the ALU, the reviewed publications are grouped into three main categories: all-optical universal gate, optical adder, and optical subtractor. All-optical universal gates provide circuit design flexibility, enable the realization of any basic logic, and minimize the number of circuit components. Conversely, optical adders and subtractors may execute complicated operations like multiplication, division, and arithmetic and logical operations. However, the photonic crystal platform has demonstrated an impressive and effective role among the several technologies used to design all-optical ALU components. Additionally, this review has taken into account both linear and non-linear photonic crystal-based devices. Each section concludes with a comparison of the devices' performance metrics and design methods. To create more effective All-optical adders based on photonic crystals for the upcoming ultra-first optical processors, some insights have been given.</p>