To be clear, a sampling rate that is only greater than the center frequency isn't very useful. You need the well known nyquist rate, twice the maximum frequency to avoid aliasing
https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampli...
For example, a signal that only has energy in the range of 9MHz to 11MHz has a center frequency of 10MHz, but a Bandwidth of 2 MHz. You could sample, and reconstruct, the signal perfectly with a sample-rate higher than 4 MHz. Any content between DC and 9MHz that would be present would distort the sampled waveform, though, and create artifacts.
https://en.wikipedia.org/wiki/Undersampling
Of course, nowadays most often one just uses a very fast ADC, and one can then choose a suitable sub-band by decimation (in a FPGA or ASIC), a kind of digital frequency filtering.
Undersampling was often used in older RF gear (and, maybe it still is for reaching the hightest frequencies? I don't know what's the current state of the art).
This is essentially like using a mixer in RF circuits. I'm pretty sure it's still used in many variations. Generally speaking you can't go high enough in sample rate to allow every RF signal (in the GHz possibly) to be sampled directly. It's always some sort of frequency shifting + filter. The key is to filter out frequencies out of the band before sampling and the band does not need to start from DC (0Hz).