Driving is a complex task involving the perception of the driving event, planning response, and action. Safe driving ensures the vehicle’s and its passengers’ safety, whereas economical driving brings down fuel consumption. Eventually, eco-safe driving that ensures economical as well as safe driving is the best bet. This review paper provides a systematic comprehensive analysis across cross-cutting dimensions such as data collection mechanisms, features affecting eco-safe driving, computational models for driving behavior analysis, driver motivational approaches towards eco-safe driving, exploiting research gaps and opportunities for further research in this domain. Driving behavior along with environmental context, including weather information, road conditions, traffic flow and time of travel, represent the most effective factors for doing eco-safe driving analysis. 82% of reviewed papers recommended OBD as a reliable data collection source, along with supplementary information from body sensors and cameras. The K-Mean clustering is an effective driving profiling technique clubbed with dimensionality reduction techniques based on Random Forest regressor, PCA and autoencoders. Deep learning and ensemble learning-based safety approaches utilizing Recurrent Convolutional Networks (RCN), Convolutional Neural Networks (CNN), and Long Short-Term Memory (LSTM) and Decision Tree (DT) have achieved impressive accuracies surpassing 99%, followed by Neural Networks (NN), Support Vector Machines (SVM) and Random Forest (RF) with accuracy ranging from 91% to 96%. Long Short-Term Memory (LSTM) yielded superior Area Under Curve (AUC of 0.836) for fuel prediction, in comparison to Support Vector Machines (SVM) and Neural Networks (NN). Gated Recurrent Unit (GRU) represents fine-grained accurate fuel-prediction methods with accuracy comparable to Long Short-Term Memory (LSTM). Prominent research gaps identified during this study are the lack of a comprehensive approach covering all aspects related to safety, fuel economy, the scope of improvement in real-time driving risk assessment at appropriate granularity level, missing effective and engaging driving feedback, dealing with uncertain and incomplete driving events, driver’s personal traits affecting driving safety and fuel-economy. The review will help in establishing the readiness of automation of driving analysis for reinforcement of eco-safe driving for various kinds of vehicles plug-in hybrid vehicles, hybrid electric vehicles, electric vehicles, and self-driving cars.