A well-known $\mathcal{N}\mathcal{P}$-hard problem from graph theory is the subgraph isomorphism problem where the goal is for given pattern and target graphs to determine whether the pattern is a subgraph of the target graph. A plethora of algorithms for solving the problem exist in literature and most of them are based on the backtracking approach. In this paper, we explore several such algorithms. In particular, we focus on algorithmic techniques as well as code tuning and optimization approaches with the goal of refining basic backtracking algorithms. We also experimentally compare the performance of algorithms in order to evaluate and demonstrate their usefulness in practice.