It's not strictly necessary to include notation-specific tempo markings, but the meaning and relative speeds change depending on what is or is not indicated.
Example: switching from 4/4 to 6/8
quarter-note = dotted quarter-note
For example, in a switch from 4/4 time to 6/8 time, one might see <quarter note> = <dotted quarter note>, which means "the pace of quarter notes in the 4/4 section will now be the pace of dotted quarter notes in 6/8 time." The tempo is considered to be unchanged, because the basic pulse — the BPM — hasn't changed; only the notation of the pulse has changed.
eighth-note = eighth-note
On the other hand, in a switch from 4/4 time to 6/8 time, one might see <eighth note> = <eighth note>, which means "keep the pace of the eighth note constant across the time-signature change." Here, the tempo will change, because what used to be 1/2 beat in 4/4 now become 1/3 beat in 6/8 time. If the original tempo was, say, 120 BPM (i.e., quarter-note = 120), the new tempo will be 80 BPM (i.e., dotted-quarter note = 80).
Another possibility is that there isn't a direct, proportional relationship during a change from 4/4 to 6/8. In that case, an explicit tempo indication is needed, such as <dotted quarter note> = 80, or <eighth note> = 96.
In the absence of a tempo indication, the presumption is that the basic pulse remains at the same tempo. That is, it would be equivalent to <quarter note> = <dotted quarter note>.