句子成分Is there anything important in today’s newspaper?

此句为there be 句型的一般疑问式。而there be 句型本身是倒装句。正常语序应为：anything important in the newspaper is there？也就是说这里anything为主语； important为后置定语修饰anything； in the newspaper介宾短语也做后置定语修饰anything； is为系动词； there为表语。

there 形式主语
is 动词
anything important 宾语
in today’s newspaper 定语

anything 主语
is 谓语
important 程度状语
in todays newspaper 状语

There be...是英语中的常见句型，表示某时某地有某物。在There be结构中，be后面的就是主语。所以，anything是主语，是不定代词，它的定语important放在了它的后面了。in today's newspaper是地点状语。