大致理了一下，归纳如下，不一定全面，希望对你有所帮助：

▲用under表示“在……下”的引申用法

1. 表示在某人的领导（指导、指挥、统治、管辖、控制等）下，通常都用under。如：

under the authority of 在…的管辖之下

This can only be done under the authority of the government minister. 这件事只有在政府部长的领导下才可以做。

under the baton of 在…的指挥下

The orchestra made the recording under the baton of a young German conductor. 管弦乐队在一位年轻的德国指挥家的带领下完成录音。

under (one’s) control 在（某人的）控制下

Everything is under control. 所有的事情都在控制中。

The city is under the control of the enemy forces. 该城现处于敌军的控制之下。

The department was under the control of Bryce Thompson. 当时这个部门归布赖斯·汤普森管。

The government has been overthrown and the country is now in / under the control of the military. 政府被推翻了，这个国家现在处于军方的控制之下。

under (a / the) dictatorship 在独裁统治之下

These men had all lived under dictatorship. 这些人都曾经在独裁统治之下生活。

under guidance / under the guidance of 在…指导下

Funds will be spent under the guidance of the committee. 基金须在该委员会指导下使用。

Under the guidance of his father, he learned how to swim. 他在父亲的指导下学会了游泳。

Volunteers are restoring the building under expert guidance. 志愿者正在专家的指导下修复这座建筑。

under sb’s leadership 在某人的领导下

The group flourished under her firm leadership. 这个团队在她的坚定领导下兴旺发达。

The school has flourished under the leadership of Mr Buxton. 学校在巴克斯顿先生的领导下越办越好。

The club prospered under Ferguson’s management. 俱乐部在弗格森的管理下蓬勃发展起来。

under rule 在…的统治下

The country remained under direct rule by the occupying powers. 这个国家仍处于占领国的直接统治之下。

under sb’s tuition 在某人的指导下

She had become expert in Chinese cooking under the tuition of her aunt. 在姑妈的指导下，她已经是烹制中餐的能手。

其他类似表达如：

under the presidency of George W. Bush 在乔治·W·布什总统的领导下

measures that were introduced under the last government 上届政府采取的措施

She held office under two different prime ministers. 她在两届不同首相的政府中任职。

It was under the emperor Justinian that these advances were made. 这些进步是在查士丁尼皇帝的统治下取得的。

2. 在压力下

under the strain 在压力下，在过度紧张下

He cracked under the strain. 他在过度紧张下崩溃了。

The ice gave way under the strain. 冰在压力作用下坍塌了。

He was breaking up under the strain. 在过度紧张下他要垮了。

under stress 在压力下

He broke under stress and had to leave. 他不堪重压，不得不离开。

Katy could think clearly when not under stress. 在没有精神压力的情况下凯蒂思路清晰。

Being under stress can cause you to miss meals, eat on the move, or bolt your food. 人在压力之下有时会吃不上饭，或边走边吃，或是匆匆吃上几口。

under pressure 在压力下

He always works best under pressure. 他总是在有压力时工作昨最好。

He only agreed to leave the country under pressure. 他是在压力下才同意出国的。

She was bound to snap under all that pressure. 在那么大的压力下她必定会垮掉。

The government will yield under pressure from the opposition. 政府会在反对派的压力下作出让步。

3. 其他表示“在…下”

under (an / the) anaesthetic 在被麻醉的状态下

It would have to be done under anaesthetic. 这个只能在麻醉的情况下做。

under cover of 在…的掩护下

They moved about under cover of darkness. 在夜幕的掩护下他们四处活动。

We attacked at night, under cover of darkness. 我们在夜幕的掩护下于晚上发动进攻。

under cross-examination在盘问之下

The defendant broke down under cross-examination. 被告在盘问下哭了起来。

under sb’s gaze 在某人的注视下

He blushed under her angry gaze. 在她的怒视下，他脸红了。

under the influence 在…的影响之下

The town grew under the influence of colonialism. 这个镇是在殖民主义的影响下发展起来的。

under (sb’s) instructions 在（…的）指示下

Under Charlemagne’s instructions, many classical texts were recopied. 遵照查理曼大帝的命令，许多经典篇章得以重新誊写。

under sb’s mediation 在某人的斡旋下

under international mediation 在国际社会的斡旋下

under oath在誓词的约束下

Witnesses must testify under oath. 证人必须在誓词的约束下作证。

under the protection of 在…的保护之下

Many British wild animals are now under the protection of the Wildlife and Countryside Act. 英国的许多野生动物现在受到《野生生物及乡野法》的保护。

under socialism 在社会主义制度下

They believed that these problems would disappear under socialism. 他们相信在社会主义制度下这些问题会消失。

under surveillance 处在监视之下：The suspects are under police surveillance. 嫌疑人在警方的监控之下。

under a cloud of suspicion 在疑云笼罩下

He ended his athletics career under a cloud of suspicion when he refused to take a drug test. 他拒绝进行药检，在疑云笼罩下结束了运动生涯。

▲不用under表示“在……下”的引申用法

against the sunset 在落日的衬托下

The trees were black against the sunset. 树木在落日的衬托下显得黑暗异常。

against a / the background 在…的背景下

The areas of water stood out against the dark background. 在黑暗背景下映衬出片片水域。

in the absence of 在缺乏…的情况下

In the absence of stone, most houses in the area are built of wood. 由于石料匮乏，这一地区的房子大多数都是用木头建造的。

in a / the climate 在…气候下

Little grows in such a dry climate. 在这种干旱的气候下很难有东西生长。

in all weathers 在任何天气情况下

The lifeboat crews go out in all weathers. 救生船人员在任何天气情况下都出动救援。

in convoy 在护卫下

The ships travelled in convoy. 这些船在护卫下航行。

in the sunlight 在阳光下

waves sparkling in the sunlight 在阳光下闪闪发光的波浪

in the sun 在阳光下

Don’t sit in the sun too long. 不要在太阳光下坐太久。

in (the) sunshine 在阳光下

The race was run in bright sunshine. 比赛在明媚的阳光下举行。

in an emergency 在紧急情况下

I need to know what to do in an emergency. 我要知道在紧急情况下该做什么。

in / under the circumstances 在某种情况下

In / Under the circumstances, you’d better ring the police. 在这种情况下你最好打电话报警。

at / on sb’s insistence 在某人的坚持下

At the insistence of his father, he bought himself a new suit. 在父亲的坚持下，他给自己买了一套新西装。

on / upon sbs recommendation 在…的建议下

I had the operation on the recommendation of my doctor. 我在医生的建议下做了手术。

at / on / upon sb’s observation 在某人的建议下

At the recommendation of a psychiatrist, the accused will remain under observation. 在精神科医生的建议下，被告会继续接受观察。

to the accompaniment of 在…的伴奏下

She sang to the accompaniment of guitars. 她在吉他的伴奏下演唱。

with the assistance of 在…的帮助下

The work was completed with the assistance of local carpenters. 这项工作在当地木匠的帮助下得以完成。

with the help of 在…的帮助下

The robbery may have been carried out with the help of a bent policeman. 抢劫有可能是在某个不良警察的帮助下得以进行的。