Which Boost features overlap with C++11?

Replaceable by C++11 language features or libraries

• Foreach → range-based for
• Functional/Forward → Perfect forwarding (with rvalue references, variadic templates and std::forward)
• In Place Factory, Typed In Place Factory → Perfect forwarding (at least for the documented use cases)
• Lambda → Lambda expression (in non-polymorphic cases)
• Local function → Lambda expression
• Min-Max → std::minmax, std::minmax_element
• Ratio → std::ratio
• Static Assert → static_assert
• Thread → <thread>, etc (but check this question).
• Typeof → auto, decltype
• Value initialized → List-initialization (§8.5.4/3)
• Math/Special Functions → <cmath>, see the list below
  • gamma function (tgamma), log gamma function (lgamma)
  • error functions (erf, erfc)
  • log1p, expm1
  • cbrt, hypot
  • acosh, asinh, atanh

TR1 (they are marked in the documentation if those are TR1 libraries)

• Array → std::array
• Bind → std::bind
• Enable If → std::enable_if
• Function → std::function
• Member Function → std::mem_fn
• Random → <random>
• Ref → std::ref, std::cref
• Regex → <regex>
• Result Of → std::result_of
• Smart Ptr → std::unique_ptr, std::shared_ptr, std::weak_ptr (but boost::intrusive_ptr still cannot be replaced)
• Swap (swapping arrays) → std::swap
• Tuple → std::tuple
• Type Traits → <type_traits>
• Unordered → <unordered_set>, <unordered_map>

Features back-ported from C++11:

• Atomic ← std::atomic
• Chrono ← <chrono> (see below)
• Move ← Rvalue references

Replaceable by C++17 language features:

• String_ref → std::string_view
• Filesystem → <filesystem> (Filesystem TS)
• Optional → std::optional (Library Fundamentals TS v1)
• Any → std::any (Library Fundamentals TS v1)
• Math/Special Functions → <cmath> (Special Math IS), see the list below
  • beta function
  • (normal / associated / spherical) Legendre polynomials
  • (normal / associated) Legendre polynomials
  • Hermite polynomials
  • Bessel (J / Y / I / K) functions (Y is called Neumann function in C++)
  • spherical Bessel (j / y) functions
  • (incomplete / complete) elliptic integrals of (first / second / third kind)
  • Riemann zeta function
  • exponential integral Ei
• Variant → std::variant (P0088R2)

The standard team is still working on it:

• Math Common Factor → std::experimetal::gcd, lcm (Library Fundamentals TS v2)
• Concept check → Concepts TS
• Range → Range TS
• Asio → Networking TS (sockets and timers only)
• Multiprecision → Numerics TS
• Coroutine/Coroutine2 → Coroutines TS

A large part of MPL can be trimmed down or removed using variadic templates. Some common use cases of Lexical cast can be replaced by std::to_string and std::stoX.

Some Boost libraries are related to C++11 but also have some more extensions, e.g. Boost.Functional/Hash contains hash_combine and related functions not found in C++11, Boost.Chrono has I/O and rounding and many other clocks, etc. so you may still want to take a look at the boost ones before really dismissing them.