The work reviews different notions of computable transformations on elementary classes of structures. We review the most prominent computable transformations, effective reducibility, computable embeddings, Turing computable embeddings, effective bi-interpretability and computable functors, discussing the different ideas behind them and their relations. Recent results on the equivalence of effective bi-interpretability and computable functors are discussed in detail and we prove that graphs and partial orders are effectively bi-interpretable and therefore share many computability theoretic properties such as degree spectra and computable dimension. At last the two recently examined notions of theory spectra and - n -spectra and their relation in context of computable transformations are examined. We show that any existing - 1 - and - 2 -spectrum can be found in the classes of graphs and partial orders.