  Machine Learning (ML), addresses a multitude of complex issues in multiple
disciplines, including social sciences, finance, and medical research. ML
models require substantial computing power and are only as powerful as the data
utilized. Due to high computational cost of ML methods, data scientists
frequently use Machine Learning-as-a-Service (MLaaS) to outsource computation
to external servers. However, when working with private information, like
financial data or health records, outsourcing the computation might result in
privacy issues. Recent advances in Privacy-Preserving Techniques (PPTs) have
enabled ML training and inference over protected data through the use of
Privacy-Preserving Machine Learning (PPML). However, these techniques are still
at a preliminary stage and their application in real-world situations is
demanding. In order to comprehend discrepancy between theoretical research
suggestions and actual applications, this work examines the past and present of
PPML, focusing on Homomorphic Encryption (HE) and Secure Multi-party
Computation (SMPC) applied to ML. This work primarily focuses on the ML model's
training phase, where maintaining user data privacy is of utmost importance. We
provide a solid theoretical background that eases the understanding of current
approaches and their limitations. In addition, we present a SoK of the most
recent PPML frameworks for model training and provide a comprehensive
comparison in terms of the unique properties and performances on standard
benchmarks. Also, we reproduce the results for some of the papers and examine
at what level existing works in the field provide support for open science. We
believe our work serves as a valuable contribution by raising awareness about
the current gap between theoretical advancements and real-world applications in
PPML, specifically regarding open-source availability, reproducibility, and
usability.
