Nowadays, gathering high-quality training data from multiple data sources with privacy preservation is a crucial challenge to training high-performance machine learning models. The potential solutions could break the barriers among isolated data corpus, and consequently enlarge the range of data available for processing. To this end, both academic researchers and industrial vendors are recently strongly motivated to propose two main-stream folders of solutions mainly based on software constructions: 1) Secure Multi-party Learning (MPL for short); and 2) Federated Learning (FL for short). The above two technical folders have their advantages and limitations when we evaluate them according to the following five criteria: security, efficiency, data distribution, the accuracy of trained models, and application scenarios. Motivated to demonstrate the research progress and discuss the insights on the future directions, we thoroughly investigate these protocols and frameworks of both MPL and FL. At first, we define the problem of Training machine learning Models over Multiple data sources with Privacy Preservation (TMMPP for short). Then, we compare the recent studies of TMMPP from the aspects of the technical routes, the number of parties supported, data partitioning, threat model, and machine learning models supported, to show their advantages and limitations. Next, we investigate and evaluate five popular FL platforms. Finally, we discuss the potential directions to resolve the problem of TMMPP in the future.