|Full name||Bozhidar Boykov Kraev|
|Date of birth||23 June 1997|
|Place of birth||Vratsa, Bulgaria|
|Height||183 cm (6 ft 0 in)|
|Playing position||Winger / Second striker|
* Senior club appearances and goals counted for the domestic league only and correct as of 6 September 2018|
‡ National team caps and goals correct as of 16 November 2018
Born in Vratsa, at the age of six Kraev began playing football at the local club Botev Vratsa, for whom his father Boyko Kraev had also played. In 2008, he joined Hristo Stoichkov's academy in Vilafranca, Spain, as a part of a Gillette programme for young talented players, which was initiated by Stoichkov. Two years later, Kraev returned to his home country to join Chavdar Etropole. Then he spent one year with his first club Botev Vratsa.
In January 2013, at the age of 15, Kraev joined Levski Sofia's academy. He made his first team debut in a 1–1 league draw against Lokomotiv Plovdiv on 19 July 2014, coming on as a second-half substitute. On 23 September, he marked his first start by scoring a hat-trick in a 7–1 away win over Spartak Varna in the Bulgarian Cup. On 14 October, Kraev was named by The Guardian as one of the forty most promising young players in the world.
On 12 December 2014, Kraev signed his first professional contract, on a three-year deal. Two days later, he was invited for a trial at Juventus. In January 2015, Kraev also spent a week on trial at English club Manchester City.
Kraev scored his first league goal for Levski in an 8–0 home win over Haskovo on 27 February 2015. On 26 May 2015, he scored his first A Group hattrick in a 6–0 win against Marek Dupnitsa. Kraev's hattrick was the 100th in Levski's history in the Bulgarian league.
On 19 June 2017, Kraev signed with Danish Superliga side Midtjylland on a five-year deal for a reported fee of €500,000. He made his debut for the team in a Europa League match against Derry City coming on as a substitute in the 73rd minute and scoring a goal 10 minutes later. On 12 April 2018, Kraev scored twice in a 2-1 win against Hobro IK and qualified his team for the cup's semifinals after coming on as a substitute in the 77th minute and scoring both goals in the game's added time. Three days later, he scored his first league goal in a 2-1 win against FC Nordsjælland.
In March 2016 Kraev was in the starting lineup of Bulgaria U19 for the 0-1 defeats from Belgium U19 and Croatia U19. On 13 May 2016 he was included in the Bulgaria U21 squad for the 2016 Toulon Tournament.
In November 2016 Kraev received his first call-up to the senior Bulgaria squad for a 2018 FIFA World Cup qualifying match against Belarus. He remained on the bench for the game. On 25 March 2017, Kraev made his complete debut for the team coming on as a substitute during the 2–0 home win over Netherlands for the 2018 FIFA World Cup qualification. On 6 September 2018, he scored 2 goals against Slovenia in the UEFA Nations' League, helping his country to 3 points.
As of 25 May 2019
|Levski Sofia||A Group||2014–15||19||6||8||3||–||–||27||9|
- Includes Bulgarian Supercup matches.
Score and result list Bulgaria's goal tally first.
|6 September 2018||Stožice Stadium, Ljubljana, Slovenia||Slovenia||
|2018–19 UEFA Nations League|
|Last updated 7 September 2018|
- FC Midtjylland
Best progressing young player in Bulgarian football - 2014, 2015
- "Чичарито от Враца" (in Bulgarian). webcafe.bg. 13 July 2011.
- "Левски привлече и по-големият брат Краев" (in Bulgarian). viasport.bg. 8 February 2013.
- "Левски - Локомотив (Пловдив) 1–1" (in Bulgarian). sportal.bg. 19 July 2014.
- "Next Generation 2014: 40 of the best young talents in world football". The Guardian. 14 October 2014.
- "Левски върза Краев с нов договор" (in Bulgarian). topsport.bg. 12 December 2014.
- "Краев замина на проби в Ювентус" (in Bulgarian). gong.bg. 15 December 2014.
- "Levski Sofia's Bozhidar Kraev arrives for Manchester City trial". theguardian.com. 4 January 2015.
- "Краев с хеттрик № 100 в историята на Левски". sportal.bg. 26 May 2015.
- "Краев влезе в историята на Левски, остави и Гунди зад себе си" (in Bulgarian). blitz.bg. 11 April 2017.
- "Bulgarsk stortalent til FC Midtjylland" (in Danish). fcm.dk. 19 June 2017.
- Божидар Краев с дебютен гол за Мидтиланд
- Отличен Краев класира отбора си на ½ финала в Дания
- Indskiftede Bozhidar Kraev blev dobbelt målscorer og matchvinder, da ulvene besejrede Hobro 2-1 i pokalkvartfinalen
- Краев отново герой, надпреварата за титлата ще е до последно
- Юношите на България аут от Евро 2016
- Юношите започнаха с минимална загуба от Хърватия
- Съставът на България U21 за международния турнир "Тулон"
- "Petar Hubchev named an expanded group for Belarus". bfunion.bg. 4 November 2016. Retrieved 7 November 2016.
- "Bulgaria NT vs. Belarus NT 1:0". flashscore.com. 13 November 2016. Retrieved 20 November 2016.
- Браво, "лъвове"! България с голям успех над Холандия
- БожиДар изстреля "лъвовете" в Словения
- "Kraev, Bozhidar". National Football Teams. Retrieved 7 September 2018.
- Dimitrov, Ivaylo (17 February 2015). "Владислав Стоянов е най-добрият български футболист за 2014 година! Лудогорци обраха почти всички индивидуални награди". topsport.bg. Retrieved 18 February 2015.