The d-th Veronese subring of a graded ring R contains the homogeneous polynomials whose degree is a multiple of d. If R is a standard graded polynomial ring, its Veronese rings have excellent features such as being determinantally presented, having quadratic Gröbner basis, and satisfying the Cohen-Macaulay and Koszul properties. In this talk we investigate to what extent analogous properties hold for R a non-standard graded polynomial ring. This is joint work with Sankhaneel Bisui, Bek Chase, Luca Fiorindo, Thiago de Holleben, Emanuela Marangone, Thai Nguyen, and Srishti Singh.