This question will likely get closed, but I'll throw in my $0.02:
Authoritative information - if you can get your hands on schematics or bills of material for these boards, the parts will be explicitly specified and you won't need to search at all. You could also try contacting technical support for the manufacturer and asking about those specific reference designators.
Context (as mentioned by @awjlogan in the comments) - having a general idea about what the chip might be doing can help you narrow down which manufacturer may or may not make it - for instance, you would not check the website of an analog IC manufacturer for digital logic gate ICs or microcontrollers.
Common marks - many larger ICs will have some form of date code (1819 in your second example is likely a date code). Very small ICs may omit it or shrink it down into a vendor-specific format. Some garden-variety SMT devices use a three-character alphanumeric code to describe the device (small transistors or MOSFETs). I don't think the characters in the embossed circles will help you those are likely batch- or process-related markings. Don't bother looking these up - focus on things which "look like" part numbers first.
Trademark symbols - many ICs will have a logo, which you can look at to match the part with its maker. Neither of your examples seem to have this, so:
Vendor names - 'PHI' on your second IC may indicate that this part was once a Philips Semiconductor part (which would be NXP / Nexperia) - it could also indicate where it was made (Phillipines).
There are just too many degrees of freedom for a sure-fire way of identifying mystery parts. Persistence and experience are necessary.
(For the record: my guess for IC #2 is a Cypress Semiconductor CG6865: "ENCORE USB COMBINATION LOW-SPEED USB AND PERIPHERAL CONTROLLER" which seems to be obsolete now. This took me less than a minute to find, knowing where to look and what to look for - this is what 20 years of experience in industry gives you!)
context
! What kind of product are they in? What are the surrounding components? For example, if you see an inductor and capacitors surrounding an IC, a good place to start looking is switch mode regulators. \$\endgroup\$