A famous problem dating back to 1911 asks whether every simple closed curve in \(\mathbb{R}^2\) has an inscribed square. It has been proved that every sufficiently smooth simple closed curve has an inscribed square, and that every simple closed curve has an inscribed rectangle. However, the answer for an inscribed square, in the general case, remains unknown. In the paper under review it is proved that, given any simple closed curve \(J\) in \(\mathbb{R}^2\) and any line \(L\), the curve \(J\) contains an incribed rhombus \(R\) with two sides parallel to \(L\). Moreover, the cyclic order of the vertices of \(R\) agrees with their cyclic order on \(J\), and the diameters of the inscribed rhombi (one for each line \(L)\) are bounded away from zero.