How to chain scope queries with OR instead of AND?

If you're looking to provide a scope (instead of explicitly working on the whole dataset) here's what you should do with Rails 5:

scope :john_or_smith, -> { where(name: "John").or(where(lastname: "Smith")) }

Or:

def self.john_or_smith
  where(name: "John").or(where(lastname: "Smith"))
end

I'm working in Rails 6 now and it seems like this is now possible. Using the queries from the OP:

# in the Person model:
scope :john, -> { where(name: "John") }
scope :smith, -> { where(lastname: "Smith") }
scope :john_or_smith, -> { john.or(self.smith) }

If you can't write out the where clause manually to include the "or" statement (ie, you want to combine two scopes), you can use union:

Model.find_by_sql("#{Model.scope1.to_sql} UNION #{Model.scope2.to_sql}")

(source: ActiveRecord Query Union)

This is will return all records matching either query. However, this returns an array, not an arel. If you really want to return an arel, you checkout this gist: https://gist.github.com/j-mcnally/250eaaceef234dd8971b.

This will do the job, as long as you don't mind monkey patching rails.

Also see these related questions: here, here and here

For rails 4, based on this article and this original answer

Person
  .unscoped # See the caution note below. Maybe you want default scope here, in which case just remove this line.
  .where( # Begin a where clause
    where(:name => "John").where(:lastname => "Smith")  # join the scopes to be OR'd
    .where_values  # get an array of arel where clause conditions based on the chain thus far
    .inject(:or)  # inject the OR operator into the arels 
    # ^^ Inject may not work in Rails3. But this should work instead:
    .joins(" OR ")
    # ^^ Remember to only use .inject or .joins, not both
  )  # Resurface the arels inside the overarching query

Note the article's caution at the end:

Rails 4.1+

Rails 4.1 treats default_scope just as a regular scope. The default scope (if you have any) is included in the where_values result and inject(:or) will add or statement between the default scope and your wheres. That's bad.

To solve that, you just need to unscope the query.

This is a very convenient way and it works fine in Rails 5:

Transaction
  .where(transaction_type: ["Create", "Correspond"])
  .or(
    Transaction.where(
      transaction_type: "Status",
      field: "Status",
      newvalue: ["resolved", "deleted"]
    )
  )
  .or(
    Transaction.where(transaction_type: "Set", field: "Queue")
  )