[sentence],换言之,[clause]
[sentence]。简言之,[clause]
换言之 and 简言之 open a clause that restates what came before. 换言之 – "change the words" – says the same thing in other terms, often spelling out what it implies. 简言之 – "brief words" – compresses a longer stretch into a short version. Both are the written, classical-flavoured forms of 换句话说 and 简单地说.
What follows 换言之 adds no new fact. It makes the previous statement concrete or draws its consequence.
A new fact after 换言之 breaks the link.
简言之 usually follows a long explanation, at the start of a new paragraph or as the last sentence of one.
总之 and 总而言之 also close a passage, gathering several points into one. 简言之 shortens a single point.
Both belong to writing and formal speech. In conversation, 换句话说, 也就是说 and 简单地说 do the same job.