The aim of this paper is to analyze the impact of the COVID-19 crisis on the business operations of small and medium-sized enterprises (SMEs) in Serbia as well as to identify the best ways to overcome the crisis effects and stimulate further SME growth. On a sample of 689 SMEs in Serbia, in the present paper we study the impact of the COVID-19 crisis on both the overall business of firms and certain aspects of their business (demand, logistics, organization of business activities, collection of trade receivables, and access to financing). The results of our research suggest that the crisis effects vary across the SME sector depending on the business activity, size, region an SME operates in, and the extent of achieved business digitalization and networking during the pandemic. Lastly, based on the effects of the COVID-19 crisis on the business operations of SMEs in Serbia and taking into account the experiences of other economies with the COVID-19 crisis as well as the lessons learned from previous crises, in this paper we highlight the significance of innovation and possible innovation responses of SMEs to the crisis effects as the ways to overcome it.