Predictive maintenance is the latest frontier in the management and maintenance of many industrial assets, including aeroengines. Made possible by last decades advances in monitoring equipment and machine learning algorithms, it permits individual-based maintenance schedules, on the basis of performance monitoring and estimates resulting from the application of diagnostic and prognostic techniques, whether on ground or real time. Predictive maintenance results in operational cost reduction and asset usage optimization, if compared with traditional maintenance strategies, which instead may suffer from unanticipated failure or unnecessary maintenance and therefore higher operational costs. In the study, Remaining Useful Life (RUL) estimates will be carried out for different turbofan engines, based on historical individual and fleet data made available by the Prognostics Center of Excellence at NASA. The design of Prognostics and Health Management (PHM) algorithms requires at first an analysis of available data to identify which of them is effectively related to equipment degradation and hence could be useful in determining future system evolution and predicting failure. In particular, RUL prediction of test engines suffering from high pressure compressor fault with exponential degradation trend has been carried out with both regression and Artificial Neural Networks (ANNs). In turn, different regression models and neural network architectures have been compared, namely tree regression with different levels of tree depth, Gaussian Process Regression (GPR) with different kernel functions and Multilayer Perceptron (MLP) with one to three hidden layers and varying number of nodes. The objective is to demonstrate the capability of such machine learning algorithms to predict engine failure and thus their importance in supporting predictive maintenance planning, and to evaluate the quality of results in relation to the algorithm structure. Results show comparable performance in terms of Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) of predicted with respect to actual RUL, in particular predictions obtained through recourse to multilayer perceptron reveal to be the most accurate, with a RMSE of 17.38 and a MAE of 12.50.