Specific testing solutions targeting blockchain-based software are gaining huge attention as blockchain technologies are being increasingly incorporated into enterprise systems. As blockchain-based software enters production systems, it is paramount to follow proper engineering practices, ensure the required level of testing, and assess the readiness of the developed system. The existing research aims at addressing the testing-related issues and challenges of engineering blockchain-based software by providing suitable techniques and tools. However, like any emerging discipline, the best practices and tools for testing blockchain-based systems are not yet sufficiently developed. In this paper, we provide a comprehensive survey on the testing of Blockchain-based Applications (BC-Apps). First, we provide a discussion on identified challenges that are associated with BCApp testing. Second, we use a layered approach to discuss the state-of-the-art testing efforts in the area of BC technologies. In particular, we present an overview of the existing testing tools and techniques that provide testing solutions either for different components at various layers of the BC-App stack or across the whole stack. Third, we provide a set of future research directions based on the identified BC testing challenges and gaps in the literature review of existing testing solutions for BC-Apps. Moreover, we reflect on the specificity of BC-based software development procedure, which makes some of the existing tools or techniques inadequate, and call for the definition of standardised testing procedures and techniques for BC-Apps. The aim of our study is to highlight the importance of BC-based software testing and to pave the way for disciplined, testable, and verifiable BC software development.