Summary: The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types: well-posedness and ill-posedness. On the well-posedness side, we show that globally \(m\)-fold symmetric vortex patches with corners emanating from the origin are globally well-posed in natural regularity classes as long as \(m\geq 3. In\) this case, all of the angles involved solve a closed ODE system which dictates the global-in-time dynamics of the corners and only depends on the initial locations and sizes of the corners. Along the way we obtain a global well-posedness result for a class of symmetric patches with boundary singular at the origin, which includes logarithmic spirals. On the ill-posedness side, we show that any other type of corner singularity in a vortex patch cannot evolve continuously in time except possibly when all corners involved have precisely the angle \(\frac{\pi}{2}\) for all time. Even in the case of vortex patches with corners of angle \(\frac{\pi}{2}\) or with corners which are only locally \(m\)-fold symmetric, we prove that they are generically ill-posed. We expect that in these cases of ill-posedness, the vortex patches actually cusp immediately in a self-similar way and we derive some asymptotic models which may be useful in giving a more precise description of the dynamics. In a companion work from 2020 on singular vortex patches [the authors, Trans. Am. Math. Soc. 373, No. 9, 6757–6775 (2020; Zbl 1454.35265)], we discuss the long-time behavior of symmetric vortex patches with corners and use them to construct patches on \(\mathbb{R}^2\) with interesting dynamical behavior such as cusping and spiral formation in infinite time.