D&D 5E Looking for clarity on casting multiple times per turn

[Lanliss]

I just hit 2nd level wizard in our last session, and want to know my capabilities. Am I able to cast more than one spell per turn? What are the restrictions on this?

In the past I remember seeing some mention of casting a second spell with a bonus action, but it had to be a cantrips? Was that in reference to a different class?

 

[AaronOfBarbaria]

There are very few circumstances under which you can cast more than one spell on your turn. Unless I've missed one, the entire list of circumstances are thus:

1) If you cast a spell that has a casting time of 1 Bonus Action, you can use your Action to cast a cantrip so long as it has a casting time of 1 action.

2) If you are multi-classed and have the Action Surge feature of the Fighter class, you can use your Action to cast a spell with 1 action casting time, then use Action Surge to cast a spell with 1 action casting time. You could even squeeze 3 spells into the same turn using Action Surge, but one would have to have a casting time of 1 Bonus Action, and the other two would have to be cantrips with a casting time of 1 action.

 

[Lanliss]

Alright, thanks for that. I will need to take a closer look at the casting time of my spells.

 

[Gadget]

I believe that there is one more case, though it does not apply to the OP:

3) Similar to option 1, if you are a sorcerer and have the quicken spell metamagic feature, you can spend sorcery points to cast a one action spell as a Bonus Action, but you can't use your Action to cast a spell outside a cantrip.

I don't have my books with me at the moment, but I think that is how it goes.

 

[S'mon]

Also you can use Reaction spells on your turn, without restriction - eg Shield if hit.

So could do:

Reaction - spell.
Bonus action - spell.
Action - cantrip.