  Federated learning (FL) is the most popular distributed machine learning
technique. FL allows machine-learning models to be trained without acquiring
raw data to a single point for processing. Instead, local models are trained
with local data; the models are then shared and combined. This approach
preserves data privacy as locally trained models are shared instead of the raw
data themselves. Broadly, FL can be divided into horizontal federated learning
(HFL) and vertical federated learning (VFL). For the former, different parties
hold different samples over the same set of features; for the latter, different
parties hold different feature data belonging to the same set of samples. In a
number of practical scenarios, VFL is more relevant than HFL as different
companies (e.g., bank and retailer) hold different features (e.g., credit
history and shopping history) for the same set of customers. Although VFL is an
emerging area of research, it is not well-established compared to HFL. Besides,
VFL-related studies are dispersed, and their connections are not intuitive.
Thus, this survey aims to bring these VFL-related studies to one place.
Firstly, we classify existing VFL structures and algorithms. Secondly, we
present the threats from security and privacy perspectives to VFL. Thirdly, for
the benefit of future researchers, we discussed the challenges and prospects of
VFL in detail.
