Submitted my CV to ASML Connection (open application). I was contacted by HR a few days later with suggested open positions deemed suitable for me based on my profile. All were in the Yieldstar Algorithms group.
After expressing my interest, my CV was forwarded to the hiring manager. A week later I was contacted by HR to arrange a time for a Skype interview with the manager. Another two weeks later the Skype interview took place.
During Skype interview the manager asked questions about my background and skills and how I evaluate them. There was also ample opportunity to ask many questions about the position/company. At the end of the call I was told I will probably be invited for an on-site interview. After about two weeks, I did not hear anything and inquired with the manager via e-mail. Shortly afterwards, HR contacted me to arrange an on-site interview. I was also asked to complete an online assessment of my personality and skills (~IQ test).
The on-site interview was about two weeks later. The planning of the travels was a bit chaotic as ASML has separate teams handling every aspect of the recruitment (HR, travel, room/time planning) and some miscommunication took place. Eventually, they arranged my trip (you should not book it yourself) one business day before the interview (taking place on Monday), after writing several e-mails.
On-site interview consisted of three, consecutive, 60 minute 1-on-1 sessions with technical staff. I was briefly greeted by the manager and then met the first interviewer. The interviews consisted of personality questions, a brief discussion of my own research topic and also technical questions to gauge my skills in areas applicable to the group. People were friendly, but one should be ready to back up everything with examples and reasons.
After the last interview session I was taken to the front door; there was no opportunity to get to know the work environment, (other) team members or the canteen etc.
One week after the on-site interview someone from HR called me to tell me they are not interested in hiring me and provided some feedback why.
Overall the interview process is very structured and professional. The administration involved in the interview process is very high, also when compared to other multi-national companies, e.g. Intel.