Circuit quantum electrodynamics with spins, or spin-circuit QED for short, is perceived as a platform for scaling up semiconductor spin qubits by enabling long-range interaction between spin qubits and dispersive spin readout. Here, I will present our latest work on spin-spin coupling through virtual microwave photons, an essential step towards resonator-mediated two-qubit gates. Previous work has demonstrated the coupling of spin qubits resonantly with the superconducting cavity, in the so-called strong coupling regime. While this is a very important first step, it is also not sufficient to allow an entangling two-qubit gate between distant spins. Using a high-impedance resonator to increase the charge-photon and spin-photon coupling, we achieve spin-spin interaction in the dispersive regime, which means that the resonator mode is only virtually populated; it is the regime where two-qubits gates are possible. We also observe photon-number splitting of the spin resonance frequency, an effect by which every resonator photon shifts the qubit frequency by more than its linewidth. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. I will then also present the latest developments on measurements in the time-domain performed on the same sample. Next, I will introduce our recent work on resolving transitions in the Jaynes-Cummings ladder. We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multi-photon transitions by increasing the probe power and using two-tone spectroscopy.