With the increase in the number of avenues for production of data everywhere including logistics, using this data has become an obvious next step. In this paper, we look at the major logistics problems in details as discussed in a seminal work in highlighting the problems in logistics by X. Li in 2014. Together with discussing the problems, we also look at the trends in solving these problems using machine learning. We look at the recent work done in the particular fields using machine learning (ML) and develop the correlation of the trends of using supervised, unsupervised and reinforcement learning in solving these problems. This correlation is developed using a table and a diagram showing ML techniques and the trends in the fields of the problems are discussed. COVID-19 has greatly accelerated these trends. This paper serves as a gentle introduction to ML techniques in the field of logistics for researchers who are new to the field.