The *Kaczmarz method* originated from the work of the Polish mathematician *Stefan Kaczmarz* [Angenäherte Auflösung von Systemen linearer Gleichungen, Bul. of the Int. Academy of Polish Sciences, 1937]. This is an iterative method designed to solve overdetermined systems $ Ax = y$ of linear equations. The algorithm works by iteratively projecting an initial guess $x_0$ onto the solution space of each equation in the system, one by one; the algorithm cycles through the rows of $A$ to update the estimate of $x$. With each step, the solution estimate gets closer to the actual solution. The method was developed as a way to efficiently solve large systems of linear equations. This situation is common in applications such as tomography and signal processing, where reconstructing a signal or image involves dealing with large datasets. Kaczmarz’s method gained importance because it avoids the need for full matrix inversion and works efficiently even when the system is inconsistent, e.g., when the right-hand side $y$ needs to be replaced by $y^\delta$ (with $||y - y^\delta|| < \delta$) due to measurement errors or noise. This is a typical feature of what are known as *Inverse Problems*. Though initially overlooked for several decades, the Kaczmarz method was rediscovered in the 1970s, particularly in the context of Computed Tomography (CT). In CT imaging, the method's ability to efficiently handle large, sparse systems made it attractive for reconstructing images from projections (a classic inverse problem). In recent years, numerous variations of the Kaczmarz method have been explored in the literature on inverse problems, e.g., Landweber Kaczmarz (LWK), Steepest-Descent Kaczmarz (SDK), expectation maximization Kaczmarz (EMK), iteratively regularized Gauss-Newton Kaczmarz (irGNK), Levenberg Marquardt Kaczmarz (LMK), iterated Tikhonov Kaczmarz (iTK), range-relaxed iterated Tikhonov Kaczmarz (rriTK), randomized Kaczmarz (rK), randomized Bregman-Kaczmarz (rBK), randomized block-sparse Kaczmarz (rbsK), stochastic Kaczmarz (sK), etc. Today, Kaczmarz type methods are regarded as fundamental iterative solvers for both linear and nonlinear systems of operator equations in Banach spaces. In this talk, we discuss some of the methods mentioned above, along with their relevant applications, ranging from CT in the 1970s to AI in the 2020s.