The development of compact and energy-efficient miniaturised lasers is a critical challenge in integrated non-linear photonics. Current research focuses on the integration of subwavelength all-dielectric lasers in CMOS compatible platforms. These systems provide a viable alternative to state-of-the-art nanoplasmonic sources, whose practicality is often hindered by high metal losses. The efficiency of dielectric nanolasers, however, is affected by the diffraction limit of light, which restricts the degree of localisation achievable with standard resonator modes. The recent development of new types of radiationless states has brought a sharp innovation in the field of subwavelength dielectric lasers. Radiationless states are exotic electromagnetic solutions that originate from the complex superposition and interaction of several resonator modes. They are associated with a high degree of near-field localisation which makes them particularly advantageous for non-linear photonics applications. In this work, we provide an overview of the most recent theoretical and experimental efforts toward the development of integrated lasers and ultrafast sources based on the amplification of exotic radiationless states. In particular, we focus our attention on two specific types of radiationless states: optical anapoles and Bound States in the Continuum (BIC). By discussing their differences and similarities, we provide a unifying view of these distinct research areas and outline possible future directions for these innovative platforms.