How are CPUs designed?
It is very likely CPU's and SoC's are used by hardware description languages like Verilog and VHDL (two major players).

These languages allow different levels of abstractions. In VHDL, you can define logic blocks as entities; it contains inputs and output ports. Within the block you can define the logic required. Say you define a block with input A, input B and output C. You could easily write C = A and B;, and basically you created a AND port block.  This is possibly the simplest block you can imagine.

Digital systems are typically designed with a strong hierarchy. One may start 'top-level' with major functions a CPU requires: proccesor (multiple?) memory, PCI-express, and other busses. Within this level busses and communication signals between memory and procesor may already be defined.

When you step one level down, it will define the innerworkings of making something 'work'. Taken an example of a microcontroller, it may contain an UART interface. The actual logic required to make a functional UART is defined one level below.. In here, much other logic may be required to generate and divide the required clock, buffer data (FIFO buffers), report data to the CPU (some kind of bus system).

The interesting thing of VHDL and digital design is the reuse of blocks. You could for example, just copy&amp;paste the UART block in your top-level to create 2 UARTs (well, maybe not that easy, only if the UART block is capable of somekind of addressing!). 

This design isn't any kind of gate-level design. The VHDL can be also be 'compiled' in a way that it is finally translated to logic gates. A machine can optimize this far better than a human could (and quicker too). 
For example; the internals of block A requires an inverter before outputting the signal. Block B takes this output signal and inverts it once again. Well, 2 inverters in series don't do much right? Correct, so you can just as well leave them out. However, in the 'top-level' design you won't be able to spot the two inverters in series.. you just see two ports connected. A compiler can optimize this far quicker than a human.

Basically what digital system design contains is the description how the logic should 'behave', and the computer is used to figure out what the most efficient way is to lay out the individual logic gates.