All roads lead to Rome is the core idea of the Japanese puzzle game Roma. It is played on an \(n \times n\) grid consisting of quadratic cells. These cells are grouped into boxes of at most four neighboring cells and are either filled, or to be filled, with arrows pointing in cardinal directions. The goal of the game is to fill the empty cells with arrows such that each box contains at most one arrow of each direction and regardless where we start, if we follow the arrows in the cells, we will always end up in the special Roma-cell. We study the computational complexity of the Japanese puzzle game Roma. We show that completing a given Roma board according to the rules is an \(\textsf {NP}\) -complete task, while counting the number of valid completions is \(\#\textsf{P}\) -complete, and determining the number of preset arrows needed to make the instance uniquely solvable is \(\varSigma _2^P\) -complete. We further show that the problem of completing a given Roma instance on an \(n\times n\) board cannot be solved in time \(\mathcal {O}\left( 2^{{o}(n)}\right) \) under ETH and give a matching dynamic programming algorithm based on the idea of Catalan structures.