In this chapter, the focus shifts to the study of linear waves and their instabilities in two-dimensional electronic systems. The chapter begins with an exploration of unstable transient responses in graphene, using a transfer matrix description to analyse the behaviour of graphene transistors. Both linear and nonlinear simulations are conducted to investigate the stability of shock waves, particularly in the context of Hugoniot and Rayleigh curves. The D’Yakov–Kontorovich instability is explored in detail, followed by a discussion of the Dyakonov–Shur instability and its application in radiation emitters. Special attention is given to the emission of THz radiation and frequency comb generation, where the influence of varying substrates is examined to optimize the instability. The chapter concludes with an analysis of magneto-plasmon instability and dynamic mode decomposition, highlighting the complex interplay between magnetic fields and instability in graphene. The chapter’s findings contribute significantly to the understanding of wave behaviour and instabilities in 2D materials, with potential applications in THz radiation devices.