There is 6502C cpu inside, running on 1.79 MHz most of the time.
Because 7800 is hybrid machine, it has two main chips: Maria (7800 mode) and old 2600's TIA (2600 mode). These two are responsible for graphics output, TIA also for sound.
For additional 128bytes of RAM, input/output ports and timers, there's RIOT chip.
Operating system is stored in ROMs.
Various other stuff is described here.
System boards and their layout is given here.

Following is the list of the released models of 7800. If you want to help me make this list complete, open your console and report me:

• the model and its TV norm
• all the COxxxxx numbers on all the parts (Uxx number, manufacturer, date YYWW)
• don't forget to add crystal values and C0xxxx numbers
• all the numbers on the board
• number of memory chips (if they're on additional board)
• all the connectors, switches etc.

board C025233-001 REV A 8427
cpu C014806C-29 8405
maria C024674-30
tia C010444D-01 C04075 8415
riot C010750-03 8415
os C024922B-29 8422
ram MCM61L16P15 8351
crystal C024912
modulator C398012-001

board C025233-002 REV B CA025234 8832
cpu C014806-35
maria C025349-001
tia C010444-31
riot UM6532 8838
os C024922B-29 8835
ram UM6116-2 8839 (2x)
crystal C024912-002
modulator C024629

board C300633-001 REV C, 9134
cpu UMC UM6502I, 9136
maria C025718-30, 9125
tia C398052-001
riot UMC UM6532, 9134
os C300558-001
ram board C300452 REV C, 9133
ram HM6168HP-70, 8522/8513, 2x
crystal 4.433618
crystal 14.187576
rgb board C301645-001 REV B, V7021 chip, 4.4333618 crystal

board C300633-001 REV C, 9134
cpu UMC UM6502I, 9137
maria C025718-30, 9134
tia C398052-001
riot UMC UM6532, 9135
os C300558-001B
ram board C300452 REV B, 8832
ram STC 2168, 8520, 2x
crystal 4.433618
crystal 14.187576
modulator C398012-001