In the year 2019, the Recommender Systems Challenge deals with a real-world task from the area of e-tourism for the first time, namely the recommendation of hotels in booking sessions. In this context, this article aims at identifying and investigating what we believe are important domain-specific challenges recommendation systems research in hotel search is facing, from both academic and industry perspectives. We focus on three main challenges, namely dealing with (1) multiple stakeholders and value-awareness in recommendations, (2) sparsity of user data and the extensive cold-start problem, and (3) dynamic input data and computational requirements. To this end, we review the state of the art toward solving these challenges and discuss shortcomings. We detail possible future directions and visions we contemplate for the further evolution of the field. This article should, therefore, serve two purposes: giving the interested reader an overview of current challenges in the field and inspiring new approaches for the ACM Recommender Systems Challenge 2019 and beyond.