The elastic flow for curves is one of the most important examples of fourth order geometric flows and it has been extensively studied in the past years. From a numerical point of view it is well known that detrimental grid deformations might occur as the curve undergoes strong deformations. In this talk I will revisit the definition of elastic flow and propose an alternative formulation whose FEM discretization provides good grid properties while being amenable for error analysis. After addressing important analytical aspects of the flow, I will cover some numerical aspects, present interesting simulations and touch upon recent related developments.