Question: As I understand, an object with mass cannot reach the speed of light because its (relativistic) mass increases "exponentially" as it approaches light speed.

So there is a relation between mass and speed. But if speed is a relative measurement (it depends on a point of reference) how does that affect the mass?  

Is the mass also relative to a point of reference?  

Or is there some absolute speed (wrt some fixed point) which affects the mass of an object?

***Follow-up***:  

What I have trouble to understand is... given these two facts (I hope I got the facts right):

1. Light always moves at the same speed (independently of the inertial
frame of reference)
2. The speed of a mass object is relative to a frame of reference

then if an object is moving at 99.999% of light-speed for a given observer, what will a different observer see?  

Will that other observer see the object moving at a different percentage of light speed?  

(assuming the observers are moving at different speeds, of course)

Answer: 
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> The speed limit is with respect to what?
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Speed is relative - this means that you have to specify which frame an object is moving with respect to. So the speed limit is with respect to whichever frame you are talking about.

E.g., Two spacecraft are moving in opposite directions at $\frac{2}{3}c$ with respect to the Earth. With respect to one of the spacecraft, however, the Earth is moving at $\frac{2}{3}c$, but the other spacecraft is *not* moving at $\frac{4}{3}c$. It is moving at a speed given by a formula called the velocity addition Lorentz transformation. The need for this Lorentz transformation arises at speeds comparable to c, due to the fact that objects travel through spacetime at a constant rate.
I don't know many equations so I think I'll give an example. Suppose you wanted to travel to the future. The best way to do so is to travel close to the speed of light. So imagine that you gear up your rocket to such a speed that for you one year in the moving rocket is equal to a million years on earth. Now from the perspective of those on earth, you need to pack in more fuel to compensate for the million minus one extra years you will be travelling. However from both perspectives (those on earth and yours) the rocket is moving at the same high speed with respect to the earth. So from your perspective you are apparently carrying enough fuel to last for a million years although your journey lasts but one year. So perhaps that's because the mass of your rocket increases due to its speed, in your perspective. In that case what fuel was used to compensate in the increase in time from the stationary (not really stationary as we mentioned the earth) point of view is used in your moving point of view to compensate for increase in mass. So I guess the mass of moving objects do increase but only from the perspective of the one moving. However this entire answer is only conjecture on my part!!