In this chapter, the primary objective is to recall the concept of a trading strategy and to extend this concept to the setting of signatures. We discuss how one can extend classical methods of optimal trading by tackling stochastic control problems through the lens of signatures, in order to incorporate path-dependencies. First introduced in (Signatures in machine learning and finance. PhD thesis, University of Oxford, 2020), the notion of a signature trading strategy allows to solve path-dependent optimization problems in a simple and explicit way. We first outline the key concepts of signature trading and highlight its associated benefits. Additionally, we present a solution to the mean-variance criterion and illustrate the advantages of signature-based methods using intuitive examples. Finally, we explore how signature trading strategies can be applied to obtain approximate solutions to optimal execution problems.