The crucial role of education in the transformation towards more sustainable and equitable societies has been increasingly recognised over the last two decades. In Spain, the integration of Sustainability into the national curriculum has been changing over time, acquiring more weight in the latest education law. This research has analysed a total of 247 curricular units of Spanish educational legislation and of STEM disciplines in Compulsory Secondary Education and Baccalaureate, to deepen the knowledge of the opportunities offered by these disciplines to address Sustainability. The results show how there is coherence between the competences required in STEM subjects and those set out in the European reference document GreenComp, highlighting the attention paid to the area related to embodying sustainability values, but detecting shortcomings in the area related to foreseeing sustainable futures. Therefore, recommendations for promoting these competences in classroom practice are included.