Altermagnets are characterized by non-relativistic alternating spin splitting in the band structure and collinear compensated magnetic moments in real space. They combine the advantages of ferromagnetic and antiferromagnetic order, exhibiting time-reversal symmetry-breaking magneto responses, vanishing stray fields and high-frequency spin dynamics. Consequently, altermagnets hold great potential for various research fields, especially for developing spintronic devices such as high-density magnetic memories and terahertz nano-oscillators. Furthermore, altermagnetism is found in a broad spectrum of materials, including metals, semiconductors, insulators and superconductors, thereby stimulating widespread interest in functional material research. In this Perspective, we provide an overview of recent experimental progress in altermagnets, focusing particularly on observations of lifted spin degeneracy via spectroscopic techniques and the resultant spin transport phenomena. Additionally, we discuss future research directions in altermagnets, encompassing fields such as spintronics, magnonics, ultrafast photonics and phononics, and properties such as superconductivity, topology and multiferroicity.