Let A = k[t] be the polynomial ring over the perfect field k and f∈A[x] be a monic irreducible separable polynomial. Denote by F/k the function field determined by f and consider a given non-zero prime ideal \mathfrak{p} of A. The Montes algorithm determines a new representation, so called OM-representation, of the prime ideals of the (finite) maximal order of F lying over \mathfrak{p}. This yields a new representation of places of function fields. In this talk we summarize briefly some applications of this new representation; that are the computation of the genus, the computation of the maximal order, and the improvement of the computation of Riemann-Roch spaces.