Axions and axion-like particles (ALPs) are among the most popular candidates that explain the origin of the mysterious dark matter. The most popular ALP production mechanism studied in the literature is the misalignment mechanism, where an ALP field with a quadratic or cosine potential has negligible kinetic energy initially, and it starts oscillating when its mass becomes comparable to the Hubble scale. Recently, there has been an interest in models that go beyond the standard assumptions. These models not only extend the ALP dark matter parameter space, but also provide a rich phenomenology which is absent in the standard scenario. In particular, the ALP fluctuations grow exponentially via parametric resonance and tachyonic instabilities. In this proceeding, we will first demonstrate why the standard paradigm cannot explain dark matter in experimentally interesting parts of the parameter space, and then we will give an overview of the alternative production mechanism with which this issue can be resolved. We will then discuss the exponential growth of the fluctuations in these models. Finally, we will comment on the observational consequences of the exponential growth and show that a sizable region of the ALP parameter space becomes testable even if ALPs have only gravitational interactions.