The importance of an efficient “Maximum Power Point Tracking (MPPT)" algorithm for a photovoltaic (PV) power generation system is undebatable. It enables the system to achieve its maximum throughput in power generation and generate the best revenue under given meteorological conditions. The non-linear relationship between output power and output voltage of a solar system gives rise to the presence of “Maximum Power Point (MPP)" at the power voltage curve, which needs to be tracked well through a proficient algorithm. This paper presents a comprehensive overview of MPPT algorithm's basic operation and the options available for its practical implementation. At first, it delineates some popular conventional MPPT algorithms including the perturbation and observation (P&O) method, incremental conductance (IC), and ripple correlation control (RCC) method. Later, the possibility of integrating state-of-the-art intelligent techniques such as fuzzy logic control (FLC), artificial neural network (ANN), particle swarm optimization (PSO), supervised, unsupervised, and reinforcement machine learning (ML) algorithms for MPPT purposes has been investigated. Operational strategies, advantages, and drawbacks of each algorithm have also been discussed. Consequently, advanced intelligence-based algorithms are found to be outperforming their conventional counterparts in terms of tracking precision, convergence speed and fluctuations at steady state. However, computational and implementational complexities associated with the most intelligence-based methods are motivating researchers to investigate hybrid solutions merging benefits of both conventional and advanced algorithms.