The domino tiling problem involves covering a flat surface, typically a rectangular grid, using rectangular dominoes that are twice as long as they are wide. Each domino can cover two adjacent squares on the grid. The challenge is to determine whether it is possible to completely cover the grid without any overlaps or gaps. This problem is a classic example in the field of combinatorial mathematics and has connections to various areas, including graph theory and algorithm design. It can be solved using different methods, such as backtracking or dynamic programming, and has applications in computer science and puzzle design.