  We explore coherent multi-photon processes in $^{87}$Rb$^{133}$Cs molecules
using 3-level lambda and ladder configurations of rotational and hyperfine
states, and discuss their relevance to future applications in quantum
computation and quantum simulation. In the lambda configuration, we demonstrate
the driving of population between two hyperfine levels of the rotational ground
state via a two-photon Raman transition. Such pairs of states may be used in
the future as a quantum memory, and we measure a Ramsey coherence time for a
superposition of these states of 58(9) ms. In the ladder configuration, we show
that we can generate and coherently populate microwave dressed states via the
observation of an Autler-Townes doublet. We demonstrate that we can control the
strength of this dressing by varying the intensity of the microwave coupling
field. Finally, we perform spectroscopy of the rotational states of
$^{87}$Rb$^{133}$Cs up to $N=6$, highlighting the potential of ultracold
molecules for quantum simulation in synthetic dimensions. By fitting the
measured transition frequencies we determine a new value of the centrifugal
distortion coefficient $D_v=h\times207.3(2)~$Hz.
