What's the most idiomatic way of working with an Iterator of Results?

There are lots of ways you could mean this.

If you just want to panic, use .map(|x| x.unwrap()).

If you want all results or a single error, collect into a Result<X<T>>:

let results: Result<Vec<i32>, _> = result_i32_iter.collect();

If you want everything except the errors, use .filter_map(|x| x.ok()) or .flat_map(|x| x).

If you want everything up to the first error, use .scan((), |_, x| x.ok()).

let results: Vec<i32> = result_i32_iter.scan((), |_, x| x.ok());

Note that these operations can be combined with earlier operations in many cases.

Since Rust 1.27, Iterator::try_for_each could be of interest:

An iterator method that applies a fallible function to each item in the iterator, stopping at the first error and returning that error.

This can also be thought of as the fallible form of for_each() or as the stateless version of try_fold().

You can implement these iterators yourself. See how filter and map are implemented in the standard library.

map_ok implementation:

#[derive(Clone)]
pub struct MapOkIterator<I, F> {
    iter: I,
    f: F,
}

impl<A, B, E, I, F> Iterator for MapOkIterator<I, F>
where
    F: FnMut(A) -> B,
    I: Iterator<Item = Result<A, E>>,
{
    type Item = Result<B, E>;

    #[inline]
    fn next(&mut self) -> Option<Self::Item> {
        self.iter.next().map(|x| x.map(&mut self.f))
    }
}

pub trait MapOkTrait {
    fn map_ok<F, A, B, E>(self, func: F) -> MapOkIterator<Self, F>
    where
        Self: Sized + Iterator<Item = Result<A, E>>,
        F: FnMut(A) -> B,
    {
        MapOkIterator {
            iter: self,
            f: func,
        }
    }
}

impl<I, T, E> MapOkTrait for I
where
    I: Sized + Iterator<Item = Result<T, E>>,
{
}

filter_ok is almost the same:

#[derive(Clone)]
pub struct FilterOkIterator<I, P> {
    iter: I,
    predicate: P,
}

impl<I, P, A, E> Iterator for FilterOkIterator<I, P>
where
    P: FnMut(&A) -> bool,
    I: Iterator<Item = Result<A, E>>,
{
    type Item = Result<A, E>;

    #[inline]
    fn next(&mut self) -> Option<Result<A, E>> {
        for x in self.iter.by_ref() {
            match x {
                Ok(xx) => if (self.predicate)(&xx) {
                    return Some(Ok(xx));
                },
                Err(_) => return Some(x),
            }
        }
        None
    }
}

pub trait FilterOkTrait {
    fn filter_ok<P, A, E>(self, predicate: P) -> FilterOkIterator<Self, P>
    where
        Self: Sized + Iterator<Item = Result<A, E>>,
        P: FnMut(&A) -> bool,
    {
        FilterOkIterator {
            iter: self,
            predicate: predicate,
        }
    }
}

impl<I, T, E> FilterOkTrait for I
where
    I: Sized + Iterator<Item = Result<T, E>>,
{
}

Your code may look like this:

["1", "2", "3", "4"]
    .iter()
    .map(|x| x.parse::<u16>().map(|a| a + 10))
    .filter_ok(|x| x % 2 == 0)
    .map_ok(|x| x + 100)
    .collect::<Result<Vec<_>, std::num::ParseIntError>>()

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