These passengers are allowed to enter:

• Nationals and residents of Switzerland or Liechtenstein;
• residents of EEA-Member country;
• some relatives of Swiss or EEA-member state citizens as the following: spouses, registered partners, children and grandchildren under 21 years, dependent ones (only children, grandchildren, parents or grandparents). They must be holders of documents proving their relationship;
• Those with a cross-border commuter permit entering Switzerland for work
• holders of a D or C visa type issued by Switzerland;
• holders of a valid Schengen visa type D may transit through Switzerland from non-Schengen country to the one issued their Schengen visa;
• holders of a vaccination certificate stating they receives the first dose of vaccine no more than 12 months before arrival. Additionaly they must have a positive PCR or rapid antigen test result taken no more than 4 weeks before receiving the first dose of vaccine. Minors may do the same without a valid vaccination certificate in case the are accompanied by fully vaccinated guardian;
• Those travelling through Switzerland directly to other country that they are allowed to entry;
• Those travelling by land to their country of origin or residency within the European Union or Schengen area. Evidence of onward journey must be presented;
•  Those passengers who have to travel to their place of work abroad with appropriate documentation; 
• Residents of the EU/EFTA area who travel for tourist purposes( tourism purpose documentation such as hotel booking to be presented);
• unmarried partners of residents of Switzerland. They must have a written invitation from the residents in Switzerland and present proof of their relationship;
• passengers arriving from
  Albania, Andorra, Armenia, Australia, Azerbaijan, Bosnia and Herzegovina, Brunei, Bulgaria, Canada, Chinese Taipei, Croatia, Cyprus, Hong Kong, Ireland, Japan, Jordan, Macao, Moldova, Monaco, New Zealand, Qatar, Romania, San Marino, Saudi Arabia, Serbia, Singapore, South Korea, Ukraine
  If they transit through third countries, then they must not leave the transit area of the airport.

Currently the following vaccines are accepted: AstraZeneca (Vaxzevria), Covishield, Janssen, Moderna, Pfizer-BioNTech, Sinopharm and Sinovac.

Every passengers before arrival must fill-in special form: contact tracing card. It may be obtained online.

Passengers entering Switzerland must have:

• a negative COVID-19 PCR or RT-PCR test result of a test taken not more than 72 hours before departure from the first embarkation point;

or

• a negative COVID-19 Rapid Antigen test result of a test taken not more than 48 hours before departure from the first embarkation point. 

This rule doesn’t apply to:

• children younger than 16 years;
• holders of a medical certificate with a positive COVID-19 test result of a test taken in the past 3 months who also have a medical discharge;
• citizens and residents of Switzerland who have completed special form stating why the test could not be taken. They will be tested for COVID-19 upon arrival. Form may be obtained online;
• holders of vaccination certificate stating that the last shot of vaccine was received before arrival.
• holders of covid recovery certificate issued no more than 6 months before arrival.

Arriving passengers could be subject fot a quarantine for 10 days. Additional info here.