In this paper, we provide a review on both fundamentals of social networks and latent space modeling. The former discusses important topics related to network description, including vertex characteristics and network structure; whereas the latter articulates relevant advances in network modeling, including random graph models, generalized random graph models, exponential random graph models, and social space models. We discuss in detail several latent space models provided in literature, providing special attention to distance, class, and eigen models in the context of undirected, binary networks. In addition, we also examine empirically the behavior of these models in terms of prediction and goodness-of-fit using more than twenty popular datasets of the network literature.