We've just had the World Championship match between Carlsen and Karjakin, so one qualifier for the next Candidates is known: Karjakin.
I assume it will be held in 2018, is anything more known about the date?
What are the rules for qualification of the other players?
The Candidates will be held in Berlin, Germany, on 10-28 March 2018 (source).
According to FIDE's Rules & Regulations for the Candidates Tournament of the FIDE World Championship cycle 2016-2018, the following will qualify, in order of priority:
1. The loser of the previous World Championship Match -- Sergey Karjakin.
2. The 2 finalists of the FIDE World Cup 2017 - Ding Liren and Levon Aronian.
This is a 128-player knockout tournament, currently being held from 1 to 25 September 2017, in Batumi, Georgia, with the final in Tbilisi, Georgia (see Wikipedia, which also has details about qualifiers to the World Cup that go too far for this answer).
Karjakin and Carlsen played the World Cup so a situation could have arisen where a player not in the final would qualify, but they were both eliminated.
Quarter finals:
Semi-finals:
Final (not relevant for the Candidates, but for completeness):
3. The top 2 winners of the FIDE Grand Prix 2016/2017.
There are four events:
Top standings after 3 events:
(players with 3 events and insufficient points left out)
4. The 2 players not otherwise qualified with the highest average rating (among those that participated in the WC or GP).
Calculated using the 12 rating lists from january 1 to december 1, 2017.
| Name | Avg | Jan | Feb | Mar | Apr | May | June| July| Aug | Sep | Oct | Nov |
|---------------------------|------|------|------|------|-----|-----|-----|-----|-----|-----|-----|-----|
| Caruana, Fabiano | 2808 | 2827 | 2827 | 2817 | 2817| 2802| 2808| 2807| 2807| 2799| 2794| 2799|
| So, Wesley | 2806 | 2808 | 2822 | 2822 | 2822| 2815| 2812| 2810| 2810| 2792| 2788| 2788|
|---------------------------|------|------|------|------|-----|-----|-----|-----|-----|-----|-----|-----|
| Vachier-Lagrave, Maxime | 2796 | 2796 | 2796 | 2803 | 2803| 2795| 2796| 2791| 2789| 2804| 2794| 2796|
| Mamedyarov, Shakhriyar | 2786 | 2766 | 2766 | 2772 | 2772| 2772| 2800| 2800| 2797| 2797| 2791| 2802|
| Nakamura, Hikaru | 2785 | 2785 | 2785 | 2793 | 2793| 2798| 2785| 2792| 2792| 2781| 2774| 2780|
| Anand, Viswanathan | 2785 | 2786 | 2786 | 2786 | 2786| 2786| 2786| 2783| 2783| 2794| 2783| 2783|
5. One organiser's nominee.
Vladimir Kramnik was chosen as the wildcard.
This could have been player with a rating of 2725 or higher in one of the rating lists in 2017.
Next update: the final Grand Prix, result 25 november.
According to Agon (who owns the rights), it will take place from March 8 to March 29, 2018.
I don't think anything else is known at this point in time.
Yes, finalist from the previous cycle is one of the candidates; two more spots go to the latest World Cup winner and runner-up, a couple of spots are determined by Grand Prix results, one spot is the host's choice (that's how Aronian got into the last Candidates), and the rest are determined by the FIDE rating list. That is, more or less, what was used for the last tournament - I don't know if that's subject to change or not.
