The present paper is a review of the main challenges faced by the management of a tertiary specialty hospital during the COVID-19 pandemic in the northern Italian region of Lombardy, an area of extremely high epidemic impact. The article focuses on the management of patient flows, access to the hospital, maintaining and reallocating staffing levels, and managing urgent referrals, information, and communications from the point of view of the hospital managers over a seven-week period. The objective of the article is to provide beneficial insights and solutions to other hospital managers and medical directors who should find themselves in the same or a similar situation. In such an epidemic emergency, in the authors' opinion, the most important factors influencing the capability of the hospital to maintain operations are (1) sustaining the strict triage of patients, (2) the differentiation of flows and pathways to create what could be regarded as "a hospital inside a hospital", (3) tracing and sharing all available information to face the rapidly changing environment, (4) being able to maintain staffing levels in critical areas by flexibly allocating the workforce, and (5) from a regional perspective, being organized along a hub-and-spoke system for critical and time-sensitive networks was key for focusing the hospital's resources on the most needed services.