The fast-paced development of laser-wakefield electron acceleration has recently culminated in the generation of electron beams with extreme characteristics, including femtosecond-scale duration, mrad divergence, and high-energy. It is now customary to attain tens to hundreds of pC of charge with an energy of hundreds of MeV per particle with small-scale commercial laser systems, with multi-GeV electron beams being demonstrated from cm-scale accelerators. The interaction of such electron beams with either a solid target or the focus of a second high-power laser can result in the generation of high-quality positron beams and MeV-photon beams. The unrivaled properties of these secondary sources make them ideal for both fundamental and practical applications. In the present article, some of their main characteristics will be discussed, with particular emphasis on their potential applications in fundamental and applied physics. A discussion of potential future developments enabled by near-term laser facilities will also be presented.