1.keep up with着重状态；意为在同时起步的条件下“跟上，赶上，不落后于”，表示同时起步，不至于掉队。它的实际含义是：与……并肩前进、并驾齐驱、保持同等地位，跟得上；跟上（人、潮流、形势等）如：
We should keep up with the times. 我们应不落伍于时代。
Can you walk a little slower? I can’t keep up with you.
你能走慢一点吗？我跟不上你。
She was skipping to keep up with him.
她连蹦带跳地走着，好跟上他的步伐。
Wages are not keeping up with inflation.
工资赶不上通货膨胀。
I can't keep up with all the changes.
我并非所有的变化都能跟得上。
Many people were holding down three jobs just to keep up with the Joneses.
许多人同时做3份工作只不过是为了和别人攀比。
Johnny finds it difficult to keep up with the rest if the class in mathematics.
约翰尼发现在数学方面很难跟上班内的其他同学。
She began to walk faster, but he lengthened his stride to keep up with her
她开始加快步子，但他加大了步幅跟着她。
She shook her head and started to walk on. He kept up with her.
她摇了摇头开始往前走。他跟了上去。
引申含义：与……保持联系；熟悉，了解（消息、形势等）；不断获知（某事的情况）
It is difficult to keep up with the rapid pace of change.
跟上迅速的变化是很困难的。
Penny tended to work through her lunch hour in an effort to keep up with her work
为了把活儿干完，彭妮常常午饭时间也要工作。
She is struggling to keep up with her schoolwork.
她在努力完成作业。
Archie liked to think he kept up with current slang.
阿奇喜欢那种紧跟潮流，讲满口时髦新词的感觉。
Even in Zurich he kept up with the County cricket scores.
即使身在苏黎世，他也一直关注着郡际板球赛的比分。
She did not bother to keep up with the news.
她不愿花时间去了解最新消息。
She kept up with the fortunes of the Reeves family
她一直关注着里夫斯家族的兴衰。
He can't keep up with others in his work.
他干活儿跟不上趟儿。
The two saleswomen were busily trying to keep up with the demand.
那两名女售货员正忙着接待顾客。
2.catch up with着重动作；表示在已经落后或起步较晚的情况下“赶上，追上”，与keep up with有区别。
He’s working hard to catch up with the others, after missing a term.
他休学了一个学期，现在正努力学习，想赶上其他同学。
He was behind in his studies because of illness, but he is catching up now.
他因为生病学习落户了，但现在正在奋起直追。
She can keep up with any other student in the class.
她能赶上班上任何一位学生。
After two weeks' absence from class，he had to study harder to catch up with his classmates.
缺课两周后，他必须更加努力学习，才能赶上同学们。
The less advanced strives to catch up with the more advanced.
后进赶先进。
We'll do our best to catch up with the advanced world levels.
我们将努力赶上世界先进水平。
In order to catch up with and surpass the advanced world levels we'll have to accelerate our speed.
要赶超世界先进水平，我们还得快马加鞭。
He stopped and let her catch up with him
他停下来，好让她追上自己。
Most late developers will catch up with their friends
大多数身材发育迟缓者都会赶上他们的朋友。
There's still time to catch up with them.
还有时间追上他们。
After a pursuit lasting all day we finally caught up with them.
经过一整天的追赶，我们终于赶上了他们。
Eventually, the army caught up with him in Latvia
最终，大部队在拉脱维亚赶上了他。
If a good runner like you can't catch up with him, how can I?
你跑得那么快还赶不上他，何况我呢？
We must exert ourselves to catch up with them, or it would be too late.
我们要急起直追，否则就太晚了。
引申含义：捕获;擒获;捉拿到；和…算旧账；使…最终尝到苦果
The law caught up with him yesterday.
昨天，他被捉拿归案。
Although he subsequently became a successful businessman, his criminal past caught up with him.
尽管后来他成了事业有成的生意人，以前的犯罪前科终究让他尝到了苦果。
She plans to return to Dublin to catch up with the relatives she has not seen since she married.
她打算回都柏林，去看望一下结婚后就再没见过面的亲戚。
The taxman caught up with him and demanded £ 7,000 in unpaid taxes
税收人员查到了他，要求他把未缴纳的7,000英镑税款交上。