Altermagnetism refers to a long-range magnetic order which intertwines with the properties of both ferromagnetism and antiferromagnetism. In this talk, we will address some of the properties of superconducting states that emerge in three-dimensional altermagnets in the presence of spin-orbit interaction. Following a weak-coupling approach, we demonstrate that such altermagnetic systems favor spin-triplet superconductivity with gap functions given in terms of a convolution of the altermagnetic order parameter itself. Consequently, this singles out f-wave spin-triplet superconductivity as the most favorable pairing state to appear in the vicinity of d-wave altermagnetism. Furthermore, we also find that the combination of spin-singlet superconducting states with altermagnetism gives rise to extended Bogoliubov-Fermi surfaces, which become protected by a Z2 topological charge. Finally, using a Ginzburg-Landau analysis, we show that, for a class of spin-orbit coupled altermagnetic models, superconductivity is expected to appear at low temperatures as an intertwined d + if state, which breaks time-reversal symmetry spontaneously.