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Why 'deshalb' and 'trotzdem' put the verb before the subject

Many German words that link two ideas look like English conjunctions: deshalb means 'so' or 'that's why', trotzdem means 'anyway' or 'nevertheless', sonst means 'otherwise'. Grammatically, though, they are adverbs. When you put one at the start of a clause, it fills the first slot of the sentence, so the conjugated verb must come next and the subject moves behind it.

English speakers tend to keep their usual subject-verb order and say deshalb ich bleibe, because 'so I stay' sounds perfectly normal in English. In German that order is wrong. The words below all work the same way, whether they express a reason, a contrast, an addition, a sequence in time or a condition.

Word list
allerdingsA2 however Allerdings ist es teuer = However, it's expensive als ErstesA2 first Als Erstes machen wir Kaffee = First of all we'll make coffee anschließendA2 afterwards Anschließend gehen wir essen = Afterwards we're going for a meal damalsA2 then Damals wohnte ich in Rom = At that time I lived in Rome danachA2 afterwards Danach gehen wir essen = Afterwards we're going for a meal endlichA2 finally Endlich ist er da = Finally he's here jedochA2 however Jedoch hat er gewonnen = However, he won nachherA2 afterwards Nachher gehen wir essen = Afterwards we're going for a meal schließlichA2 finally Schließlich hat er ja gesagt = Finally he said yes späterA2 afterwards Später gehen wir essen = Later we're going for a meal trotzdemA2 however Trotzdem hat er gewonnen = He won anyway zu der ZeitA2 then Zu der Zeit wohnte ich in Rom = Back then I lived in Rome zu dieser ZeitA2 then Zu dieser Zeit wohnte ich in Rom = At that time I lived in Rome alsoB1 so Also gehen wir = So we're going am AnfangB1 at first Am Anfang war es schwer = At the beginning it was hard andererseitsB1 on the other hand Andererseits ist es gesund = On the other hand, it's healthy anfangsB1 at first Anfangs war es schwer = At first it was hard ansonstenB1 otherwise Ansonsten verpassen wir den Zug = Otherwise we'll miss the train außerdemB1 besides Außerdem regnet es = Besides, it's raining auf der anderen SeiteB1 on the other hand Auf der anderen Seite ist es gesund = On the other hand, it's healthy dagegenB1 on the other hand Dagegen ist es teuer = On the other hand, it's expensive daherB1 so Daher ist das wichtig = That's why this is important darüber hinausB1 besides Darüber hinaus ist es billig = Furthermore, it's cheap darumB1 so Darum frage ich = That's why I'm asking deshalbB1 so Deshalb komme ich nicht = That's why I'm not coming deswegenB1 so Deswegen komme ich nicht = That's why I'm not coming erstB1 at first Erst essen wir, dann gehen wir = First we eat, then we go früherB1 previously Früher wohnte ich in Berlin = I used to live in Berlin hingegenB1 on the other hand Hingegen ist es teuer = On the other hand, it's expensive im AnschlussB1 afterwards Im Anschluss gehen wir essen = Afterwards we're going for a meal in der ZwischenzeitB1 meanwhile In der Zwischenzeit koche ich = In the meantime I'm cooking inzwischenB1 meanwhile Inzwischen wohnt sie in Wien = By now she lives in Vienna mittlerweileB1 meanwhile Mittlerweile wohnt sie in Wien = By now she lives in Vienna seitdemB1 ever since Seitdem wohnt sie hier = Since then she has lived here seitherB1 ever since Seither wohnt sie hier = Since then she has lived here sonstB1 otherwise Sonst verpassen wir den Zug = Otherwise we'll miss the train stattdessenB1 instead of Stattdessen trinke ich Tee = I drink tea instead überdiesB1 besides Überdies ist es billig = Furthermore, it's cheap übrigensB1 by the way Übrigens habe ich Zeit = By the way, I have time vorerstB1 for the time being Vorerst bleibe ich hier = For now I'm staying here vorherB1 previously Vorher rufe ich dich an = I'll call you before that vorläufigB1 for the time being Vorläufig bleibe ich hier = For the time being I'm staying here währenddessenB1 meanwhile Währenddessen koche ich = Meanwhile I'm cooking zu diesem ZeitpunktB1 then Zu diesem Zeitpunkt war ich krank = At that point I was ill zudemB1 besides Zudem ist es billig = Furthermore, it's cheap zuerstB1 at first Zuerst essen wir = First we'll eat zunächstB1 at first Zunächst war es schwer = At first it was hard zuvorB1 previously Zuvor rufe ich dich an = I'll call you before that andernfallsB2 otherwise Andernfalls verpassen wir den Zug = Otherwise we'll miss the train anfänglichB2 at first Anfänglich war es schwer = Initially it was hard unterdessenB2 meanwhile Unterdessen koche ich = Meanwhile I'm cooking zu jener ZeitB2 at that time Zu jener Zeit wohnte ich in Rom = Back then I lived in Rome
How it works

A German main clause keeps its conjugated verb in second position. The first position can hold the subject, a time phrase, an object or one of these connector adverbs. If the adverb takes position one, the verb takes position two and the subject follows the verb.

Es regnet, deshalb bleiben wir zu Hause.
(It's raining, so we're staying at home.)

In a compound tense, the auxiliary is the verb in second position and the participle goes to the end:

Ich war müde, trotzdem bin ich mitgekommen.
(I was tired; I came along anyway.)

Rule of thumb: adverb, verb, subject. Think of the adverb as taking the subject's seat, which pushes the subject behind the verb.

The words
Reason and consequence

Deshalb, deswegen, darum, daher and also all mean 'so' or 'that's why'. Daher sounds slightly more formal, and also is a false friend: it never means 'also'. Words like folglich behave the same way.

Der Zug fällt aus, also nehmen wir den Bus.
(The train is cancelled, so we're taking the bus.)
Contrast

Trotzdem, allerdings and jedoch introduce a 'however'. Andererseits, hingegen and dagegen mean 'on the other hand', and stattdessen means 'instead'. Dennoch works like trotzdem.

Das Hotel ist schön. Allerdings ist es ziemlich teuer.
(The hotel is nice. However, it's quite expensive.)
Ich trinke keinen Kaffee mehr. Stattdessen trinke ich Tee.
(I don't drink coffee anymore. I drink tea instead.)
Adding something

Außerdem, zudem, darüber hinaus and überdies mean 'besides' or 'furthermore'. The last three are more formal. Übrigens ('by the way') introduces a new point and follows the same order.

Die Wohnung ist hell. Außerdem hat sie einen Balkon.
(The flat is bright. Besides, it has a balcony.)
Time and sequence

Danach, anschließend ('afterwards'), schließlich ('finally') and vorher ('before that') order events, just like dann. Inzwischen, mittlerweile, unterdessen and währenddessen mean 'meanwhile' or 'by now', and seitdem and seither mean 'since then'.

Wir gehen erst ins Museum. Danach gehen wir essen.
(We're going to the museum first. Afterwards we're going for a meal.)
Sie ist vor drei Jahren umgezogen. Seitdem wohnt sie in Wien.
(She moved three years ago. Since then she has lived in Vienna.)
Condition

Sonst, ansonsten and andernfalls mean 'otherwise' or 'or else'.

Beeil dich, sonst verpassen wir den Zug.
(Hurry up, or else we'll miss the train.)
Watch out

Real conjunctions do not take a position in the clause. Und, aber, oder, sondern and denn stand before position one, so normal subject-verb order follows. Denn and deshalb are a classic trap because both deal with reasons:

Ich bleibe zu Hause, denn ich bin müde.
(I'm staying at home because I'm tired.)

Subordinating conjunctions send the verb to the end instead. Compare trotzdem with obwohl:

Ich bin mitgekommen, obwohl ich müde war.
(I came along although I was tired.)

Seitdem can also be used this way: seitdem sie in Wien wohnt means 'since she has lived in Vienna', with the verb at the end.

Because they are adverbs, these words can also appear later in the clause. In that case the subject comes first as usual:

Wir bleiben deshalb zu Hause.
(So we're staying at home.)

Jedoch is especially flexible. It often appears mid-clause (Er hat jedoch gewonnen), and in formal writing it can even act like aber without inversion. If you put it first with inversion, you are always correct.

Summary

When deshalb, trotzdem, sonst, außerdem, danach or any similar connector opens a clause, it fills the first position. The verb comes next and the subject follows: Deshalb komme ich nicht, never Deshalb ich komme nicht. Only true conjunctions such as und, aber, oder and denn leave the normal order unchanged.