One's current season progress can be found by going to the season page, which shows what their current season rank is, as well as how close they are to the next one. In addition, clicking on a tier shows the reward for it, as well as a description.
There are three types of tiers:
Bonus tiers, which have a single requirement of being a Gold Member
Free tiers, which can be earned by anyone
Regular tiers, which have two requirements: being a Gold Member, and completing the number of races required for the tier
All tiers, besides bonus tiers, require races to be completed in order to be earned. By doing races one levels up, which gives access to higher tiers.
Tiers can vary from 12 races - 50 races long.
The current season, Season 35, has 20 races per tier, and 40 races per Infinity tier.
The official Nitro Type news post announcing the addition of the seasons page can be found here.
There used to be leaderboards for each season where racers and teams could compete for top spots. There used to be rewards (titles and cash) for top teams and racers, but they were removed following Season 18. Titles that were given out depended on a racer's or their team's place on the leaderboard at the end of the season.
On October 18, 2020, it was announced that the season leaderboards would be removed. They were removed on January 10, 2021. 
The reason for removal was because racers were racing to the point where it was considered "unhealthy" as well as being way too competitive.
On September 22, 2016, Season 0.5 was released. This was a prototype of the new leaderboards. The old speed and races scoreboards were replaced with a new points system, that combined speed, accuracy, and races into a single score. The algorithm for how many points one earned in a single race was as follows:
(100 + (wpm / 2)) · accuracy / 100
The release of these new leaderboards pushed the Nitro Type admins to wipe out the fastest team scoreboards, and both of the all-time scoreboards.
In December 2018, during Season 18, it was announced that the season rewards would be changed so that rewards would no longer be handed out for leaderboard placement. Seasons 19 and 20 became the first seasons to follow this new system; no rewards were given out. However, Season 21 introduced a brand new rewards system, and a few similar ones have been used for every season since.
Starting in Season 26, achievements stopped having session and nitro requirements and the only requirement for achievements was just to complete races. Additionally, the admins began to increase the amount of gold-only achievements.
In a news post posted on February 27, 2020, Travis announced that more season achievement rewards would soon be added aside from the usual cars, titles, and cash. He stated that they would eventually be adding earnable emojis for use on the track (similar to the preexisting friend race emojis), custom nitro animations, sound effects, and trails. Season 27, which began on April 8, 2020, was the first season to include stickers.
On May 20, 2020, a brand new Season page was released. The season page portrayed the season achievements in a different way; rewards were given out via ranking up, rather than earning an achievement through the achievements page. All achievements earned in previous seasons would still be allowed to keep the reward, but the achievement will not appear in the “Achievements” section.
On October 18, 2020, it was announced that the leaderboards would be removed following Season 29, or on December 3.  The season leaderboards were eventually removed on January 10, 2021, after over a month of delay, and replaced with a "top teams" leaderboard which is a rolling total of the amount of races and points teams have accumulated within the past 7 days.
Before season rewards began to revolve around achievements, they were criticized due to being too repetitive (which was a result of the admins never changing the leaderboard titles). Seasons also received backlash from claims of admins "rigging" seasons (such as Seasons 1 and 14) due to bias. Today, however, many dislike seasons mainly because of seasons replacing events despite having much less effort put into them.