The limits for 401(k), 403(b), and most 457 plans will increase to $20,500 for 2022. The catch up limit for people aged 50 and over is at $6500; the total contribution can be up to $27,000. Here is the IRS release with more details: IRS announces 401(k) limit increases to $20,500
The limits for a Simple IRA contribution will increase to $14,000 for 2022. The catch up limit for people aged 50 and over is $3000; the total contribution that can be made is up $17,000. Here is the updated IRS page with more details: Retirement Topics – SIMPLE IRA Contribution Limits